A360823 - OEIS

A360823

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

1, 4, 6, 20, 10, 96, 14, 256, 288, 650, 22, 4200, 26, 4004, 11160, 18784, 34, 70758, 38, 164140, 196098, 136664, 46, 1756728, 393800, 747890, 3287844, 5452076, 58, 22563060, 62, 31220032, 50767926, 20059286, 41640130, 391194396, 74, 99622016, 725647728, 1298396440

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..40.

FORMULA

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

If p is prime, a(p) = 2 * p.

MATHEMATICA

a[n_] := DivisorSum[n, #^(n/#) * Binomial[# + n/# - 1, #] &]; Array[a, 40] (* Amiram Eldar, Jul 31 2023 *)

PROG

(PARI) my(N=50, x='x+O('x^N)); Vec(sum(k=1, N, k*x^k/(1-k*x^k)^(k+1)))