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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.

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