A363580 G.f. satisfies A(x) = exp( Sum_{k>=1} A(x^k) * x^k/(k * (1 + 2*x^k)) ).

1, 1, 0, 2, 0, 2, 1, 6, -2, 11, -1, 30, -21, 76, -60, 223, -245, 653, -817, 2031, -2935, 6521, -10067, 21455, -35425, 72152, -123756, 246752, -436854, 855852, -1546777, 3001811, -5513604, 10630676, -19747742, 37949424, -71115077, 136415279, -257301742, 493313335

Offset: 0

Author

Seiichi Manyama, Jun 10 2023

Keywords

• sign

Crossrefs

Cf. A052855, A198518, A363545, A363546, A363581.

Cf. A363578.

Programs

PARI

seq(n) = my(A=1); for(i=1, n, A=exp(sum(k=1, i, subst(A, x, x^k)*x^k/(k*(1+2*x^k)))+x*O(x^n))); Vec(A);

Formula

A(x) = (1 + 2*x) * B(x) where B(x) is the g.f. of A363578.

a(n) = A363578(n) + 2*A363578(n-1) for n > 0.