A194971 a(n) equals the coefficient of x^(2*n-1) in the n-th iteration of x+x^2 for n>=1.
1, 2, 10, 188, 8994, 832680, 127104492, 28951041456, 9201410927608, 3889680139527920, 2109876998624179100, 1428197506614652750656, 1179911974067256647171268, 1168294604146384807206421176, 1365624160842343461171218423880
Offset: 1
Keywords
Examples
The coefficients of x^k, k>=1, in the n-th iterations of x+x^2 begin: n=1: [(1), 1]; n=2: [1, 2, (2), 1]; n=3: [1, 3, 6, 9, (10), 8, 4, 1]; n=4: [1, 4, 12, 30, 64, 118, (188), 258, 302, 298, 244,162,84,32,8,1]; n=5: [1, 5, 20, 70, 220, 630, 1656, 4014, (8994), 18654, 35832,...]; n=6: [1, 6, 30, 135, 560, 2170, 7916, 27326, 89582, 279622, (832680), ...]; ... coefficients in parenthesis form the initial terms of this sequence.
Programs
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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)}