A158840 Row sums of triangle A158835.

1, 2, 7, 42, 374, 4391, 63637, 1095362, 21823226, 493898216, 12515588806, 351062669154, 10798972965266, 361471373319171, 13080119556342713, 508813238759275712, 21174032937728251318, 938646693399848483498

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, A158838, A158839.

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]); sum(k=0,n,(P~*N~^-1)[n+1, k+1])}