A363565 G.f. satisfies A(x) = exp( Sum_{k>=1} (2 * (-1)^k + A(x^k)) * x^k/k ).

1, -1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 2, 2, 1, 3, 5, 4, 4, 10, 13, 11, 16, 30, 34, 35, 58, 91, 99, 123, 200, 275, 315, 437, 671, 869, 1065, 1548, 2239, 2848, 3730, 5446, 7530, 9699, 13273, 19056, 25730, 33947, 47463, 66796, 89565, 120976, 170033, 235524

Offset

0,14

Links

Table of n, a(n) for n=0..54.

Formula

A(x) = B(x)/(1 + x)^2 where B(x) is the g.f. of A363567.

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

a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} ( 2 * (-1)^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*(-1)^k+subst(A, x, x^k))*x^k/k)+x*O(x^n))); Vec(A);

Crossrefs

Cf. A001678, A363566.

Cf. A363567.

Sequence in context: A344583 A349414 A257006 * A139687 A188181 A064581

Adjacent sequences: A363562 A363563 A363564 * A363566 A363567 A363568

Keyword

sign

Author

Seiichi Manyama, Jun 10 2023

Status

approved