A166908 Column 3 of triangle A166905.

1, 16, 270, 5148, 110929, 2677008, 71648322, 2107966432, 67649839664, 2352412120760, 88122951915388, 3538364803586104, 151611580761978784, 6905283671128114400, 333151832685664811338, 16973306740660778801468

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, A166909.

Programs

PARI

{a(n)=local(F=x, G=serreverse(x-x^2+O(x^(n+6))), M, N, P, m=n); M=matrix(m+5, m+5, r, c, F=x;for(i=1, r+c-2, F=subst(F, x, G+x*O(x^(m+5)))); polcoeff(F, c)); N=matrix(m+4, m+4, r, c, F=x;for(i=1, r, F=subst(F, x, G+x*O(x^(m+5)))); polcoeff(F, c)); P=matrix(m+4, m+4, r, c, M[r+1, c]); (P~*N~^-1)[n+4, 4]}