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A298753

Triangle read by rows, T(n,m) = Sum_{k=1..m} k*k!*(-1)^(m+k)*Stirling2(m,k)* C(2*n+k-2*m-1,n-m)/(n+k-m), for n >= 0 and 0 <= m <= n.

1, 0, 1, 0, 1, 1, 0, 2, 3, 1, 0, 5, 8, 7, 1, 0, 14, 23, 26, 15, 1, 0, 42, 70, 89, 80, 31, 1, 0, 132, 222, 302, 335, 242, 63, 1, 0, 429, 726, 1032, 1294, 1265, 728, 127, 1, 0, 1430, 2431, 3564, 4842, 5654, 4823, 2186, 255, 1, 0, 4862, 8294, 12441, 17886, 23472, 25270, 18569, 6560, 511, 1, 0, 16796, 28730, 43862, 65767, 93732

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OFFSET

0,8

LINKS

Table of n, a(n) for n=0..71.

FORMULA

E.g.f.: 1/(1+C(x)*(exp(-x*y)-1)), where C(x)=A000108(x) is the g.f. of Catalan numbers.

T(n,m) = Sum_{k=1..m} k*k!*(-1)^(m+k)*Stirling2(m,k)*C(2*n+k-2*m-1,n-m)/(n+k-m), m<n, T(n,n)=1.

T(n,m) = Sum_{k=0..n-m} (m+k)*E(m,k)*C(2*n-m-k-1,n-m-k)/n, n>m, T(n,n)=1, E(n,m) is Euler triangle A008292.

EXAMPLE

Triangle begins:

0, 1;