A338661 a(n) = Sum_{d|n} d^n * binomial(d+n/d-2, d-1).

1, 5, 28, 289, 3126, 49036, 823544, 17040385, 387538588, 10048833246, 285311670612, 8929334253419, 302875106592254, 11116754387182648, 437894348359764856, 18448995959423107073, 827240261886336764178, 39347761059781438793815, 1978419655660313589123980

Offset

1,2

Links

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

Formula

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

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

Mathematica

a[n_] := DivisorSum[n, #^n * Binomial[# + n/# - 2, #-1] &]; Array[a, 20] (* Amiram Eldar, Apr 22 2021 *)

Prog

(PARI) a(n) = sumdiv(n, d, d^n*binomial(d+n/d-2, d-1));
(PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, (k*x/(1-(k*x)^k))^k))

Crossrefs

Cf. A023887, A157019, A157020, A324158, A324159, A339481, A339482, A339712, A343573.

Sequence in context: A171187 A354899 A057792 * A174464 A372163 A354897

Adjacent sequences: A338658 A338659 A338660 * A338662 A338663 A338664

Keyword

nonn

Author

Seiichi Manyama, Apr 22 2021

Status

approved