User:Peter Luschny/IndexGeneralStirling1

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.