A269957 Triangle read by rows, T(n,k) = Sum_{j=k..n} A269940(n,j)*A269939(j,k), for n>=0 and 0<=k<=n.

1, 0, 1, 0, 5, 9, 0, 41, 210, 225, 0, 469, 5115, 14175, 11025, 0, 6889, 142492, 763350, 1455300, 893025, 0, 123605, 4566149, 41943090, 146522250, 212837625, 108056025, 0, 2620169, 166939742, 2462128095, 13973628900, 35936814375, 42141849750, 18261468225

Offset: 0

Author

Peter Luschny, Mar 27 2016

Keywords

• nonn
• tabl

Examples

			Triangle starts:
[1]
[0, 1]
[0, 5, 9]
[0, 41, 210, 225]
[0, 469, 5115, 14175, 11025]
[0, 6889, 142492, 763350, 1455300, 893025]
		

Crossrefs

Cf. A001818, A032188, A269939, A269940.

Programs

Sage

F = lambda n,k,f: sum((-1)^(m+k)*binomial(n+k,n+m)*f(n+m,m) for m in (0..k))
T = lambda n,k: sum(F(n, j, stirling_number1)*F(j, k, stirling_number2) for j in (k..n))
for n in (0..6): print([T(n, k) for k in (0..n)])

Formula

T(n,n) = A001818(n).

T(n,1) = A032188(n+1) for n>=1.