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A336989 Expansion of Product_{k>=1} (1 + x^k / (1 - k*x)). 2
1, 1, 2, 5, 13, 36, 107, 343, 1184, 4391, 17448, 74082, 335131, 1610301, 8191728, 43973853, 248305235, 1470474074, 9107950029, 58856529464, 395914407606, 2766669954699, 20047716439541, 150384068021507, 1166037568730402, 9332538119883810, 77004693701288392, 654279226353488820 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
FORMULA
G.f.: exp(Sum_{k>=1} x^k * Sum_{d|k} (-1)^(d+1) / (d * (1 - k/d * x)^d)).
MATHEMATICA
m = 27; CoefficientList[Series[Product[1 + x^k/(1 - k*x), {k, 1, m}], {x, 0, m}], x] (* Amiram Eldar, Aug 10 2020 *)
PROG
(PARI) N=40; x='x+O('x^N); Vec(prod(k=1, N, 1+x^k/(1-k*x)))
(PARI) N=40; x='x+O('x^N); Vec(exp(sum(k=1, N, x^k*sumdiv(k, d, (-1)^(d+1)/(d*(1-k/d*x)^d)))))
CROSSREFS
Sequence in context: A135337 A133365 A135335 * A066723 A000994 A266546
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Aug 10 2020
STATUS
approved

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Last modified March 29 04:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)