A360824 Expansion of Sum_{k>0} (k * x)^k / (1 - k * x^k)^(k+1).

1, 6, 30, 284, 3130, 47082, 823550, 16782664, 387422928, 10000094720, 285311670622, 8916102486528, 302875106592266, 11112006871683606, 437893890382576560, 18446744074918103056, 827240261886336764194, 39346408075331452862196

Offset

1,2

Links

Table of n, a(n) for n=1..18.

Formula

a(n) = Sum_{d|n} d^(d+n/d-1) * binomial(d+n/d-1,d).

If p is prime, a(p) = p + p^p.

Mathematica

a[n_] := DivisorSum[n, #^(# + n/# - 1) * Binomial[# + n/# - 1, #] &]; Array[a, 20] (* Amiram Eldar, Jul 31 2023 *)

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, (k*x)^k/(1-k*x^k)^(k+1)))
(PARI) a(n) = sumdiv(n, d, d^(d+n/d-1)*binomial(d+n/d-1, d));

Crossrefs

Cf. A339712, A343574, A360823.

Sequence in context: A215288 A295611 A264641 * A110374 A360831 A232978

Adjacent sequences: A360821 A360822 A360823 * A360825 A360826 A360827

Keyword

nonn

Author

Seiichi Manyama, Feb 22 2023

Status

approved