A363474 G.f. satisfies A(x) = exp( 2 * Sum_{k>=1} (-1)^(k+1) * A(-x^k) * x^k/k ).
1, 2, -3, -14, 22, 138, -213, -1536, 2474, 18928, -31451, -248992, 420804, 3416514, -5844716, -48349920, 83503128, 700674606, -1219159874, -10345673158, 18109290380, 155082913608, -272798814028, -2353889042848, 4157686512816, 36104006239798
Offset: 0
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..1000
Programs
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PARI
seq(n) = my(A=1); for(i=1, n, A=exp(2*sum(k=1, i, (-1)^(k+1)*subst(A, x, -x^k)*x^k/k)+x*O(x^n))); Vec(A);
Formula
A(x) = Sum_{k>=0} a(k) * x^k = Product_{k>=0} (1+x^(k+1))^(2 * (-1)^k * a(k)).
a(0) = 1; a(n) = (2/n) * Sum_{k=1..n} ( Sum_{d|k} d * (-1)^(d+k/d) * a(d-1) ) * a(n-k).