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.

A284830 Expansion of Sum_{i>=1} x^(i^2)/(1 - x^(i^2)) * Product_{j>=i} 1/(1 - x^(j^2)).

This page as a plain text file.
%I A284830 #10 Apr 05 2017 04:46:57
%S A284830 1,2,3,5,6,8,10,14,16,19,23,30,33,38,44,55,60,69,77,93,102,113,126,
%T A284830 148,162,177,198,226,246,268,293,334,361,392,424,480,516,556,601,668,
%U A284830 721,773,835,917,990,1054,1129,1239,1325,1415,1508,1649,1757,1875,1990,2157,2303,2441,2595,2796
%N A284830 Expansion of Sum_{i>=1} x^(i^2)/(1 - x^(i^2)) * Product_{j>=i} 1/(1 - x^(j^2)).
%C A284830 Total number of smallest parts in all partitions of n into squares (A000290).
%H A284830 <a href="/index/Par#partN">Index entries for related partition-counting sequences</a>
%F A284830 G.f.: Sum_{i>=1} x^(i^2)/(1 - x^(i^2)) * Product_{j>=i} 1/(1 - x^(j^2)).
%e A284830 a(9) = 16 because we have [9], [4, 4, 1], [4, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 1] and 1 + 1 + 5 + 9 = 16.
%t A284830 nmax = 60; Rest[CoefficientList[Series[Sum[x^i^2/(1 - x^i^2) Product[1/(1 - x^j^2), {j, i, nmax}], {i, 1, nmax}], {x, 0, nmax}], x]]
%o A284830 (PARI) x='x+O('x^61); Vec(sum(i=1, 60, x^i^2/(1 - x^i^2) * prod(j=i, 60, 1/(1 - x^j^2)))) \\ _Indranil Ghosh_, Apr 04 2017
%Y A284830 Cf. A000290, A001156, A092268, A092269, A195820, A281541.
%K A284830 nonn
%O A284830 1,2
%A A284830 _Ilya Gutkovskiy_, Apr 03 2017