A363579 G.f. satisfies A(x) = exp( Sum_{k>=1} ((-3)^k + A(x^k)) * x^k/k ).

1, -2, 5, -11, 27, -70, 188, -502, 1355, -3712, 10269, -28546, 79777, -224153, 632581, -1791644, 5091109, -14510079, 41464784, -118773034, 340950420, -980660721, 2825700987, -8155455450, 23573749136, -68236663474, 197774787066, -573915774310, 1667300177595

Offset

0,2

Links

Table of n, a(n) for n=0..28.

Formula

A(x) = B(x)/(1 + 3*x) where B(x) is the g.f. of A363581.

A(x) = Sum_{k>=0} a(k) * x^k = 1/(1+3*x) * 1/Product_{k>=0} (1-x^(k+1))^a(k).

a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} ( (-3)^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, ((-3)^k+subst(A, x, x^k))*x^k/k)+x*O(x^n))); Vec(A);

Crossrefs

Cf. A001678, A036249, A362389, A363541, A363578.

Cf. A363581.

Sequence in context: A238825 A073225 A027087 * A055227 A325916 A257790

Adjacent sequences: A363576 A363577 A363578 * A363580 A363581 A363582

Keyword

sign

Author

Seiichi Manyama, Jun 10 2023

Status

approved