A327249 - OEIS

%I #17 Sep 08 2022 08:46:24

%S 1,2,1,5,1,14,1,17,28,26,1,160,1,50,251,321,1,622,1,1607,1030,122,1,

%T 6257,3126,170,2917,12202,1,27291,1,28929,6656,290,84036,117721,1,362,

%U 13183,407121,1,417881,1,220100,850312,530,1,2246465,823544,2100626

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

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

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

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

%o (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

%o (PARI) a(n) = sumdiv(n, d, (n/d)^(d-1) * binomial(n/d,d-1)); \\ _Michel Marcus_, Sep 15 2019

%Y Cf. A006005 (positions of 1's), A087909, A217668, A260180, A327238.

%K nonn

%O 1,2

%A _Ilya Gutkovskiy_, Sep 15 2019