A158839 Column 3 of triangle A158835.

1, 4, 34, 412, 6325, 116372, 2483706, 60168736, 1628677692, 48672911296, 1590752204044, 56418074957840, 2157411204773415, 88464995576660084, 3871611011946560294, 180101399407072883012, 8873328068327122625596

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).

Crossrefs

Cf. A158835, A158836, A158837, A158836, A158840.

Programs

PARI

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