A187556 Triangle read by rows of products of (signless) Stirling numbers of the first kind (A132393) and Stirling numbers of the second kind (A008277).

1, 0, 1, 0, 1, 1, 0, 2, 9, 1, 0, 6, 77, 36, 1, 0, 24, 750, 875, 100, 1, 0, 120, 8494, 20250, 5525, 225, 1, 0, 720, 111132, 488824, 257250, 24500, 441, 1, 0, 5040, 1659636, 12685512, 11514069, 2058000, 85652, 784, 1, 0, 40320, 27943920, 357325100, 522796680, 156042999, 12002256, 252252, 1296, 1, 0, 362880, 524580336, 10941291000, 24681106400, 11453045625, 1444332771, 55566000, 652500, 2025, 1

Offset

0,8

Links

Table of n, a(n) for n=0..65.

Formula

Formula: a(n,k) = s(n,k)*S(n,k), where the s(n,k) are the (signless) Stirling numbers of the first kind and the S(n,k) are the Stirling numbers of the second kind.

Example

Triangle begins:
1
0,1
0,1,1
0,2,9,1
0,6,77,36,1
0,24,750,875,100,1
0,120,8494,20250,5525,225,1
0,720,111132,488824,257250,24500,441,1
0,5040,1659636,12685512,11514069,2058000,85652,784,1

Maple

seq(seq(abs(combinat[stirling1](n, k))*combinat[stirling2](n, k), k=0..n), n=0..8);

Mathematica

Flatten[Table[Table[Abs[StirlingS1[n, k]]*StirlingS2[n, k], {k, 0, n}], {n, 0, 8}] , 1]

Prog

(Maxima) create_list(abs(stirling1(n, k)*stirling2(n, k)), n, 0, 10, k, 0, n);

Crossrefs

Cf. A132393, A008277

Sequence in context: A248853 A272003 A128892 * A198103 A105548 A153093

Adjacent sequences: A187553 A187554 A187555 * A187557 A187558 A187559

Keyword

nonn,easy,tabl

Author

Emanuele Munarini, Mar 11 2011

Status

approved