cp's OEIS Frontend

A324159 Expansion of Sum_{k>=1} k * x^k / (1 - k * x^k)^k.

%I A324159 #31 Sep 03 2019 12:08:41
%S A324159 1,3,4,13,6,58,8,137,172,296,12,2063,14,1254,5536,7697,18,25201,20,
%T A324159 68976,70862,23882,24,607485,218776,108720,918568,1810089,30,6746147,
%U A324159 32,9408545,11779582,2233172,19935756,102405280,38,9968370,145283360,393585971,42,730233631,44,1296043651,2718300016
%N A324159 Expansion of Sum_{k>=1} k * x^k / (1 - k * x^k)^k.
%H A324159 Seiichi Manyama, <a href="/A324159/b324159.txt">Table of n, a(n) for n = 1..5000</a>
%F A324159 a(n) = Sum_{d|n} (n/d)^d * binomial(n/d+d-2,d-1).
%F A324159 a(p) = p + 1, where p is prime.
%t A324159 nmax = 45; CoefficientList[Series[Sum[k x^k/(1 - k x^k)^k, {k, 1, nmax}], {x, 0, nmax}], x] // Rest
%t A324159 Table[Sum[(n/d)^d Binomial[n/d + d - 2, d - 1], {d, Divisors[n]}], {n, 1, 45}]
%o A324159 (PARI) a(n) = sumdiv(n, d, (n/d)^d * binomial(n/d+d-2, d-1)); \\ _Michel Marcus_, Sep 02 2019
%o A324159 (PARI) N=66; x='x+O('x^N); Vec(sum(k=1, N, k*x^k/(1-k*x^k)^k)) \\ _Seiichi Manyama_, Sep 03 2019
%Y A324159 Cf. A055225, A087909, A157019, A157020, A324158.
%K A324159 nonn
%O A324159 1,2
%A A324159 _Ilya Gutkovskiy_, Sep 02 2019