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Triangle a(n,k) read by rows: product s(n,k)*s(n+1,k+1) of Stirling numbers of the first kind.
1

%I #8 Mar 30 2012 18:55:29

%S 1,0,1,0,3,1,0,22,18,1,0,300,385,60,1,0,6576,11250,2975,150,1,0,

%T 211680,444976,165375,14875,315,1,0,9408960,23164848,10992856,1440600,

%U 56350,588,1,0,552303360,1543644432,883573488,151957281,8890560,175812,1008,1,0,41391544320,128509156800,85483976320,18121263300,1420415577,42865200,475020,1620,1

%N Triangle a(n,k) read by rows: product s(n,k)*s(n+1,k+1) of Stirling numbers of the first kind.

%H Vincenzo Librandi, <a href="/A187558/b187558.txt">Table of n, a(n) for n = 0..495</a>

%F a(n,k) = A048994(n,k)*A048994(n+1,k+1) = A132393(n,k)*A132393(n+1,k+1).

%e Triangle begins:

%e 1

%e 0,1

%e 0,3,1

%e 0,22,18,1

%e 0,300,385,60,1

%e 0,6576,11250,2975,150,1

%e 0,211680,444976,165375,14875,315,1

%e 0,9408960,23164848,10992856,1440600,56350,588,1

%e 0,552303360,1543644432,883573488,151957281,8890560,175812,1008,1

%p seq(seq(combinat[stirling1](n,k)*combinat[stirling1](n+1,k+1),k=0..n),n=0..8);

%t Table[StirlingS1[n, k]StirlingS1[n + 1, k + 1], {n, 0, 8}, {k, 0, 8}]//MatrixForm

%o (Maxima) create_list(stirling1(n,k)*stirling1(n+1,k+1),n,0,10,k,0,n);

%K nonn,easy,tabl

%O 0,5

%A _Emanuele Munarini_, Mar 11 2011