A327249 - OEIS

A327249

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

1, 2, 1, 5, 1, 14, 1, 17, 28, 26, 1, 160, 1, 50, 251, 321, 1, 622, 1, 1607, 1030, 122, 1, 6257, 3126, 170, 2917, 12202, 1, 27291, 1, 28929, 6656, 290, 84036, 117721, 1, 362, 13183, 407121, 1, 417881, 1, 220100, 850312, 530, 1, 2246465, 823544, 2100626

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..50.

FORMULA

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

MATHEMATICA

nmax = 50; CoefficientList[Series[Sum[x^k (1 + k x^k)^k, {k, 1, nmax}], {x, 0, nmax}], x] // Rest

Table[DivisorSum[n, (n/#)^(# - 1) Binomial[n/#, # - 1] &], {n, 1, 50}]

PROG

(Magma) [&+[(n div d)^(d-1)*Binomial(n div d, d-1):d in Divisors(n)]:n in [1..50]]; // Marius A. Burtea, Sep 15 2019