A158840 - OEIS

%I #2 Mar 30 2012 18:37:16

%S 1,2,7,42,374,4391,63637,1095362,21823226,493898216,12515588806,

%T 351062669154,10798972965266,361471373319171,13080119556342713,

%U 508813238759275712,21174032937728251318,938646693399848483498

%N Row sums of triangle A158835.

%C 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).

%o (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])}

%Y Cf. A158835, A158836, A158837, A158838, A158839.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Mar 28 2009