

A284899


Expansion of Product_{k>=1} 1/(1+x^k)^(k^5) in powers of x.


5



1, 1, 31, 212, 284, 4935, 43719, 160002, 96747, 4914512, 31358932, 94515285, 97642670, 2823746182, 16834776254, 51617810512, 11233909783, 1137004349695, 7267899354808, 25263858110877, 24537905293857, 319397811973578, 2523465326904492
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OFFSET

0,3


LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..2647


FORMULA

a(0) = 1, a(n) = (1/n)*Sum_{k=1..n} A284927(k)*a(nk) for n > 0.  Seiichi Manyama, Apr 06 2017


MATHEMATICA

CoefficientList[Series[Product[1/(1 + x^k)^(k^5) , {k, 40}], {x, 0, 40}], x] (* Indranil Ghosh, Apr 05 2017 *)


PROG

(PARI) x= 'x + O('x^40); Vec(prod(k=1, 40, 1/(1 + x^k)^(k^5))) \\ Indranil Ghosh, Apr 05 2017


CROSSREFS

Cf. A248884.
Product_{k>=1} 1/(1+x^k)^(k^m): A081362 (m=0), A255528 (m=1), A284896 (m=2), A284897 (m=3), A284898 (m=4), this sequence (m=5).
Sequence in context: A164784 A290008 A121616 * A062393 A183792 A183784
Adjacent sequences: A284896 A284897 A284898 * A284900 A284901 A284902


KEYWORD

sign


AUTHOR

Seiichi Manyama, Apr 05 2017


STATUS

approved



