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%I #8 Feb 19 2018 03:35:43
%S 1,1,1,2,1,3,6,2,3,13,24,6,6,13,71,120,24,18,26,71,461,720,120,72,78,
%T 142,461,3447,5040,720,360,312,426,922,3447,29093,40320,5040,2160,
%U 1560,1704,2766,6894,29093,273343,362880,40320,15120,9360,8520,11064,20682
%N Triangle T(n,k) = A000142(n-k)*A003319(k+1) read by rows.
%F Row sums: Sum_{k=0..n} T(n,k) = A000142(n+1) = (n+1)!.
%e The triangle starts at row n=0 with columns 0 <= k <= n:
%e 1;
%e 1, 1;
%e 2, 1, 3;
%e 6, 2, 3, 13;
%e 24, 6, 6, 13, 71;
%e 120, 24, 18, 26, 71, 461;
%t (* b = A003319 *) b[0]=0; b[n_] := b[n] = n! - Sum[k!*b[n-k], {k, 1, n-1}];
%t T[n_, k_] := (n-k)! b[k+1]; Table[T[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* _Jean-François Alcover_, Feb 18 2018 *)
%K nonn,tabl
%O 0,4
%A _Paul Curtz_, Aug 09 2008
%E Edited and extended by _R. J. Mathar_, Dec 05 2008
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