A363508 G.f. satisfies A(x) = exp( Sum_{k>=1} (4 + A(x^k)) * x^k/k ).

1, 5, 20, 80, 340, 1516, 7046, 33736, 165436, 826566, 4193348, 21542664, 111848161, 585949358, 3093526496, 16442687695, 87914559018, 472522551440, 2551591234444, 13836226412386, 75311992329508, 411336641019998, 2253641429297336

Offset

0,2

Links

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

Formula

A(x) = Sum_{k>=0} a(k) * x^k = 1/(1-x)^4 * 1/Product_{k>=0} (1-x^(k+1))^a(k).

a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} ( 4 + 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, (4+subst(A, x, x^k))*x^k/k)+x*O(x^n))); Vec(A);

Crossrefs

Cf. A000081, A029857, A036249, A363507.

Cf. A363510.

Sequence in context: A170686 A003947 A369837 * A252698 A271196 A033131

Adjacent sequences: A363505 A363506 A363507 * A363509 A363510 A363511

Keyword

nonn

Author

Seiichi Manyama, Jun 06 2023

Status

approved