A363475 G.f. satisfies A(x) = exp( 3 * Sum_{k>=1} (-1)^(k+1) * A(-x^k) * x^k/k ).
1, 3, -6, -44, 96, 918, -2073, -22278, 52629, 597627, -1451736, -17065641, 42205373, 508415817, -1273766637, -15623442097, 39528583206, 491601500847, -1253383246330, -15759867676416, 40430096479776, 512914242127868, -1322511998532891
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(3*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))^(3 * (-1)^k * a(k)).
a(0) = 1; a(n) = (3/n) * Sum_{k=1..n} ( Sum_{d|k} d * (-1)^(d+k/d) * a(d-1) ) * a(n-k).