A166909 Row sums of triangle A166905.

1, 2, 11, 97, 1145, 16796, 293623, 5950792, 137075837, 3535416136, 100902444181, 3156570232069, 107392381479683, 3947409366073512, 155880018189733841, 6581149438442041483, 295807451972657856921, 14102499966460374953016

Offset: 0

Author

Paul D. Hanna, Nov 28 2009

Keywords

• nonn

Comments

Triangle A166905 transforms rows into diagonals in the table A158825 of coefficients in successive iterations of x*Catalan(x) (cf. A000108).

Crossrefs

Cf. A166905, A158831, A166906, A166907, A166908.

Programs

PARI

{a(n)=local(F=x, G=serreverse(x-x^2+O(x^(n+3))), M, N, P, m=n); M=matrix(m+2, m+2, r, c, F=x;for(i=1, r+c-2, F=subst(F, x, G+x*O(x^(m+3)))); polcoeff(F, c)); N=matrix(m+1, m+1, r, c, F=x;for(i=1, r, F=subst(F, x, G+x*O(x^(m+3)))); polcoeff(F, c)); P=matrix(n+1, n+1, r, c, M[r+1, c]); M=(P~*N~^-1); sum(k=1,n+1,M[n+1,k])}