A187557 Triangle read by rows of products of Stirling numbers of the second kind (A008277): a(n,k) = S(n,k) S(n+1,k+1).

1, 0, 1, 0, 3, 1, 0, 7, 18, 1, 0, 15, 175, 60, 1, 0, 31, 1350, 1625, 150, 1, 0, 63, 9331, 31500, 9100, 315, 1, 0, 127, 60858, 512001, 367500, 37240, 588, 1, 0, 255, 384175, 7505820, 11823651, 2778300, 122892, 1008, 1, 0, 511, 2379150, 103167625, 330419250, 158670477, 15558480, 346500, 1620, 1, 0, 1023, 14564011, 1359847500, 8414726650, 7632684675, 1460631249, 69854400, 866250, 2475, 1

Offset: 0

Author

Emanuele Munarini, Mar 11 2011

Keywords

• nonn
• easy
• tabl

Examples

			Triangle begins:
1
0,1
0,3,1
0,7,18,1
0,15,175,60,1
0,31,1350,1625,150,1
0,63,9331,31500,9100,315,1
0,127,60858,512001,367500,37240,588,1
0,255,384175,7505820,11823651,2778300,122892,1008,1
		

Crossrefs

Cf. A008277

Programs

Maple

seq(seq(combinat[stirling2](n,k)*combinat[stirling2](n+1,k+1),k=0..n),n=0..8);

Mathematica

Table[StirlingS2[n, k]StirlingS2[n + 1, k + 1], {n, 0, 8}, {k, 0, 8}]//MatrixForm

Maxima

create_list(stirling2(n,k)*stirling2(n+1,k+1),n,0,10,k,0,n);