A363471 G.f. satisfies A(x) = exp( 3 * Sum_{k>=1} A(-x^k) * x^k/k ).

1, 3, -3, -26, 48, 444, -920, -9126, 19587, 204214, -449496, -4841001, 10856283, 119585034, -271813440, -3044796399, 6991433415, 79341313335, -183641493481, -2105713558467, 4905239040894, 56722082044512, -132833292089826, -1546827734185557

Offset: 0

Author

Seiichi Manyama, Jun 03 2023

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A006964, A200402, A363470.

Programs

PARI

seq(n) = my(A=1); for(i=1, n, A=exp(3*sum(k=1, i, subst(A, x, -x^k)*x^k/k)+x*O(x^n))); Vec(A);

Formula

A(x) = B(x)^3 where B(x) is the g.f. of A200402.

A(x) = Sum_{k>=0} a(k) * x^k = 1/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-1) * a(d-1) ) * a(n-k).