A363541 G.f. satisfies A(x) = exp( Sum_{k>=1} (3^k + A(x^k)) * x^k/k ).

1, 4, 17, 73, 324, 1469, 6838, 32490, 157398, 775010, 3870690, 19567202, 99957231, 515250057, 2676884745, 14002926871, 73693381322, 389904743248, 2072794614996, 11066421965311, 59310040841395, 318978744562253, 1720962766007827

Offset

0,2

Links

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

Formula

A(x) = B(x)/(1 - 3*x) where B(x) is the g.f. of A363546.

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.

Cf. A363507, A363543, A363546.

Sequence in context: A018902 A344506 A339042 * A184700 A125586 A086351

Adjacent sequences: A363538 A363539 A363540 * A363542 A363543 A363544

Keyword

nonn

Author

Seiichi Manyama, Jun 09 2023

Status

approved