A338685 a(n) = Sum_{d|n} d^n * binomial(d, n/d).

1, 8, 81, 1040, 15625, 282123, 5764801, 134610944, 3486804084, 100097656250, 3138428376721, 107025924222976, 3937376385699289, 155582338242342053, 6568408660888671875, 295155786482995691520, 14063084452067724991009, 708240750793407501694308, 37589973457545958193355601

Offset

1,2

Links

Winston de Greef, Table of n, a(n) for n = 1..384

Formula

G.f.: Sum_{k >= 1} ((1 + (k * x)^k)^k - 1).

If p is prime, a(p) = p^(p+1).

Mathematica

a[n_] := DivisorSum[n, #^n * Binomial[#, n/#] &]; Array[a, 20] (* Amiram Eldar, Apr 24 2021 *)

Prog

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

Crossrefs

Cf. A023887, A318636, A327238, A338684, A338693.

Sequence in context: A065440 A338694 A318047 * A092366 A022519 A138439

Adjacent sequences: A338682 A338683 A338684 * A338686 A338687 A338688

Keyword

nonn

Author

Seiichi Manyama, Apr 23 2021

Status

approved