cp's OEIS Frontend

A194971 a(n) equals the coefficient of x^(2*n-1) in the n-th iteration of x+x^2 for n>=1.

%I A194971 #8 Mar 30 2012 18:37:28
%S A194971 1,2,10,188,8994,832680,127104492,28951041456,9201410927608,
%T A194971 3889680139527920,2109876998624179100,1428197506614652750656,
%U A194971 1179911974067256647171268,1168294604146384807206421176,1365624160842343461171218423880
%N A194971 a(n) equals the coefficient of x^(2*n-1) in the n-th iteration of x+x^2 for n>=1.
%e A194971 The coefficients of x^k, k>=1, in the n-th iterations of x+x^2 begin:
%e A194971 n=1: [(1), 1];
%e A194971 n=2: [1, 2, (2), 1];
%e A194971 n=3: [1, 3, 6, 9, (10), 8, 4, 1];
%e A194971 n=4: [1, 4, 12, 30, 64, 118, (188), 258, 302, 298, 244,162,84,32,8,1];
%e A194971 n=5: [1, 5, 20, 70, 220, 630, 1656, 4014, (8994), 18654, 35832,...];
%e A194971 n=6: [1, 6, 30, 135, 560, 2170, 7916, 27326, 89582, 279622, (832680), ...]; ...
%e A194971 coefficients in parenthesis form the initial terms of this sequence.
%o A194971 (PARI) {a(n)=local(A=x,G=x+x^2); for(i=1,n, A=subst(G, x, A+x*O(x^(2*n)))); polcoeff(A, 2*n-1)}
%Y A194971 Cf. A194972, A122888, A112317.
%K A194971 nonn
%O A194971 1,2
%A A194971 _Paul D. Hanna_, Sep 06 2011