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%I #2 Mar 30 2012 18:37:18
%S 1,9,108,1610,28560,586320,13658904,355787568,10243342296,
%T 322939137312,11063339361360,409194048521778,16249995494795920,
%U 689585033717023224,31140529927119263136,1490994828293677370148,75444108490820383882392
%N Column 2 of triangle A166905.
%C Triangle A166905 transforms rows into diagonals in the table A158825 of coefficients in successive iterations of x*Catalan(x) (cf. A000108).
%o (PARI) {a(n)=local(F=x, G=serreverse(x-x^2+O(x^(n+5))), M, N, P, m=n); M=matrix(m+4, m+4, r, c, F=x;for(i=1, r+c-2, F=subst(F, x, G+x*O(x^(m+4)))); polcoeff(F, c)); N=matrix(m+3, m+3, r, c, F=x;for(i=1, r, F=subst(F, x, G+x*O(x^(m+4)))); polcoeff(F, c)); P=matrix(m+3, m+3, r, c, M[r+1, c]); (P~*N~^-1)[n+3, 3]}
%Y Cf. A166905, A158831, A166906, A166908, A166909.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Nov 28 2009
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