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.

A339235 G.f.: Sum_{k>=0} x^(k^4) / Product_{j=1..k^4} (1 - x^j).

This page as a plain text file.
%I A339235 #14 Dec 05 2020 14:42:58
%S A339235 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,3,4,6,8,12,16,23,31,43,57,78,102,
%T A339235 136,177,232,297,384,487,621,781,984,1226,1531,1892,2340,2872,3524,
%U A339235 4294,5232,6335,7666,9229,11099,13288,15893,18929,22519,26695,31604,37293
%N A339235 G.f.: Sum_{k>=0} x^(k^4) / Product_{j=1..k^4} (1 - x^j).
%C A339235 Number of partitions of n such that the number of parts is a fourth power.
%C A339235 Also number of partitions of n such that the largest part is a fourth power.
%H A339235 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A339235 a(18) = 3 because we have [18], [3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] and [2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] (see the first comment) or[16, 2], [16, 1, 1] and [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] (see the second comment).
%t A339235 nmax = 57; CoefficientList[Series[Sum[x^(k^4)/Product[1 - x^j, {j, 1, k^4}], {k, 0, Floor[nmax^(1/4)] + 1}], {x, 0, nmax}], x]
%Y A339235 Cf. A000583, A046042, A089333, A334626.
%K A339235 nonn
%O A339235 0,17
%A A339235 _Ilya Gutkovskiy_, Dec 05 2020