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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).

%I A187557 #8 Jun 02 2025 03:58:42
%S A187557 1,0,1,0,3,1,0,7,18,1,0,15,175,60,1,0,31,1350,1625,150,1,0,63,9331,
%T A187557 31500,9100,315,1,0,127,60858,512001,367500,37240,588,1,0,255,384175,
%U A187557 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
%N 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).
%e A187557 Triangle begins:
%e A187557 1
%e A187557 0,1
%e A187557 0,3,1
%e A187557 0,7,18,1
%e A187557 0,15,175,60,1
%e A187557 0,31,1350,1625,150,1
%e A187557 0,63,9331,31500,9100,315,1
%e A187557 0,127,60858,512001,367500,37240,588,1
%e A187557 0,255,384175,7505820,11823651,2778300,122892,1008,1
%p A187557 seq(seq(combinat[stirling2](n,k)*combinat[stirling2](n+1,k+1),k=0..n),n=0..8);
%t A187557 Table[StirlingS2[n, k]StirlingS2[n + 1, k + 1], {n, 0, 8}, {k, 0, 8}]//MatrixForm
%o A187557 (Maxima) create_list(stirling2(n,k)*stirling2(n+1,k+1),n,0,10,k,0,n);
%Y A187557 Cf. A008277
%K A187557 nonn,easy,tabl
%O A187557 0,5
%A A187557 _Emanuele Munarini_, Mar 11 2011