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# User:Peter Luschny/IndexGeneralStirling1

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Generalized Stirling_1 Triangle k = -6 | ||||

Sum: A049402 | all partitions: A144356 | ~ by length: A049374 | ~ by biggest part: A157386 | diagonal: A001725 |

1 | [1] | [1] | [1] | 1 |

1 | [1] | [1] | [1] | 1 |

7 | [1,6] | [6,1] | [1,6] | 6 |

61 | [1,18,42] | [42,18,1] | [1,18,42] | 42 |

649 | [1,36,108,168,336] | [336,276,36,1] | [1,144,168,336] | 336 |

8245 | [1,60,540,420,2520,1680,3024] | [3024,4200,960,60,1] | [1,600,2940,1680,3024] | 3024 |

Generalized Stirling_1 Triangle k = -5 | ||||

Sum: A049378 | all partitions: A144355 | ~ by length: A049353 | ~ by biggest part: A157385 | diagonal: A001720 |

1 | [1] | [1] | [1] | 1 |

1 | [1] | [1] | [1] | 1 |

6 | [1,5] | [5,1] | [1,5] | 5 |

46 | [1,15,30] | [30,15,1] | [1,15,30] | 30 |

436 | [1,30,75,120,210] | [210,195,30,1] | [1,105,120,210] | 210 |

4956 | [1,50,375,300,1500,1050,1680] | [1680,2550,675,50,1] | [1,425,1800,1050,1680] | 1680 |

Generalized Stirling_1 Triangle k = -4 | ||||

Sum: A049377 | all partitions: A144354 | ~ by length: A049352 | ~ by biggest part: A157384 | diagonal: A001715 |

1 | [1] | [1] | [1] | 1 |

1 | [1] | [1] | [1] | 1 |

5 | [1,4] | [4,1] | [1,4] | 4 |

33 | [1,12,20] | [20,12,1] | [1,12,20] | 20 |

273 | [1,24,48,80,120] | [120,128,24,1] | [1,72,80,120] | 120 |

2721 | [1,40,240,200,800,600,840] | [840,1400,440,40,1] | [1,280,1000,600,840] | 840 |

Generalized Stirling_1 Triangle k = -3 | ||||

Sum: A049376 | all partitions: A144353 | ~ by length: A046089 | ~ by biggest part: A157383 | diagonal: A001710 |

1 | [1] | [1] | [1] | 1 |

1 | [1] | [1] | [1] | 1 |

4 | [1,3] | [3,1] | [1,3] | 3 |

22 | [1,9,12] | [12,9,1] | [1,9,12] | 12 |

154 | [1,18,27,48,60] | [60,75,18,1] | [1,45,48,60] | 60 |

1306 | [1,30,135,120,360,300,360] | [360,660,255,30,1] | [1,165,480,300,360] | 360 |

Generalized Stirling_1 Triangle k = -2 | ||||

Sum: A000262 | all partitions: A130561 | ~ by length: A105278 | ~ by biggest part: A157400 | diagonal: A000142 |

1 | [1] | [1] | [1] | 1 |

1 | [1] | [1] | [1] | 1 |

3 | [1,2] | [2,1] | [1,2] | 2 |

13 | [1,6,6] | [6,6,1] | [1,6,6] | 6 |

73 | [1,12,12,24,24] | [24,36,12,1] | [1,24,24,24] | 24 |

501 | [1,20,60,60,120,120,120] | [120,240,120,20,1] | [1,80,180,120,120] | 120 |

Generalized Stirling_1 Triangle k = -1 | ||||

Sum: A000142 | all partitions: A102189 | ~ by length: A008275 | ~ by biggest part: A126074 | diagonal: A000142 |

1 | [1] | [1] | [1] | 1 |

1 | [1] | [1] | [1] | 1 |

2 | [1,1] | [1,1] | [1,1] | 1 |

6 | [1,3,2] | [2,3,1] | [1,3,2] | 2 |

24 | [1,6,3,8,6] | [6,11,6,1] | [1,9,8,6] | 6 |

120 | [1,10,15,20,20,30,24] | [24,50,35,10,1] | [1,25,40,30,24] | 24 |

Generalized Stirling_1 Triangle k = 0 | ||||

Sum: A000012 | all partitions: A155972 | ~ by length: A023531 | ~ by biggest part: A000000 | diagonal: A000000 |

1 | [1] | [1] | [1] | 1 |

1 | [1] | [1] | [1] | 1 |

1 | [1,0] | [0,1] | [1,0] | 0 |

1 | [1,0,0] | [0,0,1] | [1,0,0] | 0 |

1 | [1,0,0,0,0] | [0,0,0,1] | [1,0,0,0] | 0 |

1 | [1,0,0,0,0,0,0] | [0,0,0,0,1] | [1,0,0,0,0] | 0 |

Generalized Stirling_1 Triangle k = 1 | ||||

Sum: A000085 | all partitions: A144357 | ~ by length: A049403 | ~ by biggest part: A157391 | diagonal: A130716 |

1 | [1] | [1] | [1] | 1 |

1 | [1] | [1] | [1] | 1 |

2 | [1,1] | [1,1] | [1,1] | 1 |

4 | [1,3,0] | [0,3,1] | [1,3,0] | 0 |

10 | [1,6,3,0,0] | [0,3,6,1] | [1,9,0,0] | 0 |

26 | [1,10,15,0,0,0,0] | [0,0,15,10,1] | [1,25,0,0,0] | 0 |

Generalized Stirling_1 Triangle k = 2 | ||||

Sum: A049425 | all partitions: A144358 | ~ by length: A049404 | ~ by biggest part: A157392 | diagonal: A008279 |

1 | [1] | [1] | [1] | 1 |

1 | [1] | [1] | [1] | 1 |

3 | [1,2] | [2,1] | [1,2] | 2 |

9 | [1,6,2] | [2,6,1] | [1,6,2] | 2 |

33 | [1,12,12,8,0] | [0,20,12,1] | [1,24,8,0] | 0 |

141 | [1,20,60,20,40,0,0] | [0,40,80,20,1] | [1,80,60,0,0] | 0 |

Generalized Stirling_1 Triangle k = 3 | ||||

Sum: A049426 | all partitions: A144877 | ~ by length: A049410 | ~ by biggest part: A157393 | diagonal: A008279 |

1 | [1] | [1] | [1] | 1 |

1 | [1] | [1] | [1] | 1 |

4 | [1,3] | [3,1] | [1,3] | 3 |

16 | [1,9,6] | [6,9,1] | [1,9,6] | 6 |

76 | [1,18,27,24,6] | [6,51,18,1] | [1,45,24,6] | 6 |

436 | [1,30,135,60,180,30,0] | [0,210,195,30,1] | [1,165,240,30,0] | 0 |

Generalized Stirling_1 Triangle k = 4 | ||||

Sum: A049427 | all partitions: A144878 | ~ by length: A049424 | ~ by biggest part: A157394 | diagonal: A008279 |

1 | [1] | [1] | [1] | 1 |

1 | [1] | [1] | [1] | 1 |

5 | [1,4] | [4,1] | [1,4] | 4 |

25 | [1, 12, 12] | [12, 12, 1] | [1, 12, 12] | 12 |

145 | [1,24,48,48,24] | [24,96,24,1] | [1,72,48,24] | 24 |

1025 | [1,40,240,120,480,120,24] | [24,600,360,40,1] | [1,280,600,120,24] | 24 |

Generalized Stirling_1 Triangle k = 5 | ||||

Sum: A049431 | all partitions: A144879 | ~ by length: A049411 | ~ by biggest part: A157395 | diagonal: A008279 |

1 | [1] | [1] | [1] | 1 |

1 | [1] | [1] | [1] | 1 |

6 | [1,5] | [5,1] | [1,5] | 5 |

36 | [1,15,20] | [20,15,1] | [1,15,20] | 20 |

246 | [1,30,75,80,60] | [60,155,30,1] | [1,105,80,60] | 60 |

2046 | [1,50,375,200,1000,300,120] | [120,1300,575,50,1] | [1,425,1200,300,120] | 120 |

Note: If no exact match could be found a reference was given which contains useful hints and links related to the sequence.

An index for generalized Stirling2 triangles.