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Column 3 of triangle A166900.
4

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

%S 1,16,230,3564,61845,1207696,26415840,642448632,17240108314,

%T 506777596248,16210958231104,560988459704192,20891752852722701,

%U 833382707754108896,35461362393617267808,1603581518693484768464

%N Column 3 of triangle A166900.

%C Triangle A166900 transforms rows into diagonals in the table of coefficients of successive iterations of x+x^2 (cf. A122888).

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

%Y Cf. A166900, A166901, A166902, A166904, A122888, A135080.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Nov 27 2009