A166906 Column 1 of triangle A166905.

1, 4, 33, 380, 5510, 95732, 1933288, 44437080, 1144564278, 32638644236, 1020503373032, 34708182795156, 1275532011982176, 50365443858930384, 2126358227959866224, 95577781657788563192, 4556923094838105968302

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, A166907, A166908, A166909.

Programs

PARI

{a(n)=local(F=x, G=serreverse(x-x^2+O(x^(n+4))), M, N, P, m=n); M=matrix(m+3, m+3, 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+2, m+2, r, c, F=x;for(i=1, r, F=subst(F, x, G+x*O(x^(m+3)))); polcoeff(F, c)); P=matrix(m+2, m+2, r, c, M[r+1, c]); (P~*N~^-1)[n+2, 2]}