A363567 G.f. satisfies A(x) = exp( Sum_{k>=1} A(x^k) * x^k/(k * (1 + x^k)^2) ).

1, 1, 0, 1, 1, 0, 1, 2, 1, 1, 3, 3, 2, 4, 7, 7, 7, 12, 17, 17, 22, 37, 47, 51, 73, 110, 133, 162, 242, 339, 412, 545, 798, 1065, 1342, 1860, 2648, 3474, 4547, 6400, 8874, 11665, 15754, 22152, 30205, 40201, 55301, 77115, 104463, 141087, 195669, 270620, 366902

Offset: 0

Author

Seiichi Manyama, Jun 10 2023

Keywords

• nonn

Crossrefs

Cf. A198518, A363575.

Cf. A363547, A363565.

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)^2))+x*O(x^n))); Vec(A);

Formula

A(x) = (1 + x)^2 * B(x) where B(x) is the g.f. of A363565.

a(n) = Sum_{k=0..2} binomial(2,k) * A363565(n-k).