A327238 Expansion of Sum_{k>=1} ((1 + k * x^k)^k - 1).

1, 4, 9, 20, 25, 63, 49, 160, 108, 350, 121, 940, 169, 1225, 1475, 2304, 289, 7560, 361, 8025, 12446, 7139, 529, 58192, 3750, 13858, 61965, 102655, 841, 191181, 961, 318464, 220704, 40460, 354172, 1304370, 1369, 63175, 629863, 4012608, 1681, 1916733, 1849

Offset: 1

Author

Ilya Gutkovskiy, Sep 14 2019

Keywords

• nonn
• look

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A055225, A056045, A318636, A327124.

Programs

Mathematica

nmax = 43; CoefficientList[Series[Sum[((1 + k x^k)^k - 1), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
Table[DivisorSum[n, (n/#)^# Binomial[n/#, #] &], {n, 1, 43}]

PARI

a(n)={sumdiv(n, d, (n/d)^d * binomial(n/d,d))} \\ Andrew Howroyd, Sep 14 2019

Formula

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

a(p) = p^2, where p is prime.