A158836 Column 0 of triangle A158835.

1, 1, 4, 27, 254, 3062, 45052, 783151, 15712342, 357459042, 9094926988, 255939571048, 7893741230500, 264806871279676, 9600056691219936, 374033821840909263, 15586672520501193866, 691789220336675178652

Offset: 0

Author

Paul D. Hanna, Mar 28 2009

Keywords

• nonn

Comments

Triangle A158835 transforms diagonals in the array A158825 of coefficients of successive iterations of x*C(x) where C(x) is the Catalan function (A000108).

Links

• Paul D. Hanna, Table of n, a(n), n = 0..50.

Crossrefs

Cf. A158835, A158837, A158838, A158839, A158840.

Programs

PARI

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