cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A319670 a(n) = [x^n] Product_{k>=2} 1/(1 - x^k)^n.

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%I A319670 #10 Oct 06 2018 08:03:28
%S A319670 1,0,2,3,14,30,119,301,1078,3036,10242,30624,100451,310128,1004817,
%T A319670 3158343,10182982,32345186,104145896,332953929,1072383374,3442913407,
%U A319670 11100120528,35742258497,115377720235,372326184555,1203406838428,3890040945078,12588182588373,40748118469180
%N A319670 a(n) = [x^n] Product_{k>=2} 1/(1 - x^k)^n.
%C A319670 Number of partitions of n into parts > 1, if there are n kinds of parts.
%H A319670 Vaclav Kotesovec, <a href="/A319670/b319670.txt">Table of n, a(n) for n = 0..1000</a>
%F A319670 a(n) =  [x^n] exp(n*Sum_{k>=1} (sigma(k) - 1)*x^k/k).
%F A319670 a(n) ~ c * d^n / sqrt(n), where d = 3.293558598422332665054219310876308... and c = 0.2154241499279313950113565475... - _Vaclav Kotesovec_, Oct 06 2018
%t A319670 Table[SeriesCoefficient[Product[1/(1 - x^k)^n , {k, 2, n}], {x, 0, n}], {n, 0, 29}]
%t A319670 Table[SeriesCoefficient[((1 - x)/QPochhammer[x])^n, {x, 0, n}], {n, 0, 29}]
%t A319670 Table[SeriesCoefficient[Exp[n Sum[(DivisorSigma[1, k] - 1) x^k/k, {k, 1, n}]], {x, 0, n}], {n, 0, 29}]
%Y A319670 Cf. A000203, A002865, A008485, A147766, A191659, A304625, A319671.
%K A319670 nonn
%O A319670 0,3
%A A319670 _Ilya Gutkovskiy_, Sep 25 2018