A363578 G.f. satisfies A(x) = exp( Sum_{k>=1} ((-2)^k + A(x^k)) * x^k/k ).

1, -1, 2, -2, 4, -6, 13, -20, 38, -65, 129, -228, 435, -794, 1528, -2833, 5421, -10189, 19561, -37091, 71247, -135973, 261879, -502303, 969181, -1866210, 3608664, -6970576, 13504298, -26152744, 50758711, -98515611, 191517618, -372404560, 725061378

Offset

0,3

Links

Table of n, a(n) for n=0..34.

Formula

A(x) = B(x)/(1 + 2*x) where B(x) is the g.f. of A363580.

A(x) = Sum_{k>=0} a(k) * x^k = 1/(1+2*x) * 1/Product_{k>=0} (1-x^(k+1))^a(k).

a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} ( (-2)^k + Sum_{d|k} d * a(d-1) ) * a(n-k).

Prog

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

Crossrefs

Cf. A001678, A036249, A362389, A363541, A363579.

Cf. A363580.

Sequence in context: A188538 A282164 A268175 * A209025 A346779 A153955

Adjacent sequences: A363575 A363576 A363577 * A363579 A363580 A363581

Keyword

sign

Author

Seiichi Manyama, Jun 10 2023

Status

approved