A158836 - OEIS

%I #5 Mar 30 2012 18:37:16

%S 1,1,4,27,254,3062,45052,783151,15712342,357459042,9094926988,

%T 255939571048,7893741230500,264806871279676,9600056691219936,

%U 374033821840909263,15586672520501193866,691789220336675178652

%N Column 0 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).

%H Paul D. Hanna, <a href="/A158836/b158836.txt">Table of n, a(n), n = 0..50.</a>

%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]); (P~*N~^-1)[n+1,1]}

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

%K nonn

%O 0,3

%A _Paul D. Hanna_, Mar 28 2009