A360712 Expansion of Sum_{k>0} (k * x * (1 + k*x^k))^k.

1, 5, 27, 272, 3125, 46915, 823543, 16781312, 387421218, 10000078125, 285311670611, 8916102153177, 302875106592253, 11112006865911623, 437893890381640625, 18446744074783358976, 827240261886336764177, 39346408075327943829273

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..386

Formula

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

If p is an odd prime, a(p) = p^p.

Mathematica

a[n_] := DivisorSum[n, #^(#+n/#-1) * Binomial[#, n/# - 1] &]; Array[a, 20] (* Amiram Eldar, Aug 09 2023 *)

Prog

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

Crossrefs

Cf. A217668, A327249, A338693, A359700, A360618.

Sequence in context: A266204 A360770 A360726 * A300621 A265907 A360732

Adjacent sequences: A360709 A360710 A360711 * A360713 A360714 A360715

Keyword

nonn

Author

Seiichi Manyama, Feb 17 2023

Status

approved