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

Author

Emanuele Munarini, Mar 11 2011

Keywords

• nonn
• easy
• tabl

Examples

			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
		

Crossrefs

Cf. A132393, A008277

Programs

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]

Maxima

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

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.