login
A324159
Expansion of Sum_{k>=1} k * x^k / (1 - k * x^k)^k.
9
1, 3, 4, 13, 6, 58, 8, 137, 172, 296, 12, 2063, 14, 1254, 5536, 7697, 18, 25201, 20, 68976, 70862, 23882, 24, 607485, 218776, 108720, 918568, 1810089, 30, 6746147, 32, 9408545, 11779582, 2233172, 19935756, 102405280, 38, 9968370, 145283360, 393585971, 42, 730233631, 44, 1296043651, 2718300016
OFFSET
1,2
LINKS
FORMULA
a(n) = Sum_{d|n} (n/d)^d * binomial(n/d+d-2,d-1).
a(p) = p + 1, where p is prime.
MATHEMATICA
nmax = 45; CoefficientList[Series[Sum[k x^k/(1 - k x^k)^k, {k, 1, nmax}], {x, 0, nmax}], x] // Rest
Table[Sum[(n/d)^d Binomial[n/d + d - 2, d - 1], {d, Divisors[n]}], {n, 1, 45}]
PROG
(PARI) a(n) = sumdiv(n, d, (n/d)^d * binomial(n/d+d-2, d-1)); \\ Michel Marcus, Sep 02 2019
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Sep 02 2019
STATUS
approved