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

%I

%S 1,2,10,188,8994,832680,127104492,28951041456,9201410927608,

%T 3889680139527920,2109876998624179100,1428197506614652750656,

%U 1179911974067256647171268,1168294604146384807206421176,1365624160842343461171218423880

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

%e The coefficients of x^k, k>=1, in the n-th iterations of x+x^2 begin:

%e n=1: [(1), 1];

%e n=2: [1, 2, (2), 1];

%e n=3: [1, 3, 6, 9, (10), 8, 4, 1];

%e n=4: [1, 4, 12, 30, 64, 118, (188), 258, 302, 298, 244,162,84,32,8,1];

%e n=5: [1, 5, 20, 70, 220, 630, 1656, 4014, (8994), 18654, 35832,...];

%e n=6: [1, 6, 30, 135, 560, 2170, 7916, 27326, 89582, 279622, (832680), ...]; ...

%e coefficients in parenthesis form the initial terms of this sequence.

%o (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 Cf. A194972, A122888, A112317.

%K nonn

%O 1,2

%A _Paul D. Hanna_, Sep 06 2011

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Last modified May 13 22:47 EDT 2021. Contains 343868 sequences. (Running on oeis4.)