A363575 G.f. satisfies A(x) = exp( Sum_{k>=1} A(x^k) * x^k/(k * (1 + x^k)^3) ).

1, 1, -1, 1, 2, -4, -1, 10, -3, -20, 19, 38, -70, -65, 221, 73, -640, 117, 1745, -1223, -4433, 5770, 10124, -22007, -18999, 75063, 19307, -235725, 59665, 685744, -525477, -1832544, 2531982, 4364936, -10007555, -8468154, 35302510, 8542655, -114305453

Offset: 0

Author

Seiichi Manyama, Jun 10 2023

Keywords

• sign

Crossrefs

Cf. A198518, A363567.

Cf. A363548, A363566.

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+x^k)^3))+x*O(x^n))); Vec(A);

Formula

A(x) = (1 + x)^3 * B(x) where B(x) is the g.f. of A363566.

a(n) = Sum_{k=0..3} binomial(3,k) * A363566(n-k).