%I #2 Mar 30 2012 18:37:18

%S 1,2,11,97,1145,16796,293623,5950792,137075837,3535416136,

%T 100902444181,3156570232069,107392381479683,3947409366073512,

%U 155880018189733841,6581149438442041483,295807451972657856921,14102499966460374953016

%N Row sums of triangle A166905.

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

%o (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])}

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

%K nonn

%O 0,2

%A _Paul D. Hanna_, Nov 28 2009