A363507 G.f. satisfies A(x) = exp( Sum_{k>=1} (3 + A(x^k)) * x^k/k ).

1, 4, 14, 50, 191, 763, 3180, 13640, 59937, 268304, 1219626, 5614038, 26117296, 122598622, 579977691, 2762264225, 13234003724, 63737225733, 308406648979, 1498558628584, 7309116199687, 35772044402485, 175621484712091, 864670723348447

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

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

Crossrefs

Cf. A000081, A029857, A036249, A363508.

Cf. A363509.

Sequence in context: A272687 A076024 A062807 * A117421 A034743 A096241

Adjacent sequences: A363504 A363505 A363506 * A363508 A363509 A363510

Keyword

nonn

Author

Seiichi Manyama, Jun 06 2023

Status

approved