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.

A303942 Number of partitions of n into at most 1 copy of 1^2, 2 copies of 2^2, 3 copies of 3^2, ... .

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%I A303942 #20 May 04 2018 11:05:07
%S A303942 1,1,0,0,1,1,0,0,1,2,1,0,0,1,1,0,1,2,2,1,1,1,1,1,1,3,3,2,1,2,2,1,2,3,
%T A303942 4,3,3,2,2,2,2,4,4,4,3,4,3,2,3,5,7,5,5,5,6,4,3,6,8,8,5,6,6,6,6,7,9,9,
%U A303942 10,8,8,7,8,10,11,12,10,11,10,10,9,12,15,14,14
%N A303942 Number of partitions of n into at most 1 copy of 1^2, 2 copies of 2^2, 3 copies of 3^2, ... .
%H A303942 Seiichi Manyama, <a href="/A303942/b303942.txt">Table of n, a(n) for n = 0..1000</a>
%F A303942 G.f.: Product_{k>=1} (1-x^(k^2*(k+1)))/(1-x^(k^2)).
%e A303942    n |              | a(n)
%e A303942 -----+--------------+------
%e A303942    1 | 1            |  1
%e A303942    4 | 4            |  1
%e A303942    5 | 4+1          |  1
%e A303942    8 | 4+4          |  1
%e A303942    9 | 9, 4+4+1     |  2
%e A303942   10 | 9+1          |  1
%e A303942   13 | 9+4          |  1
%e A303942   14 | 9+4+1        |  1
%e A303942   16 | 16           |  1
%e A303942   17 | 16+1, 9+4+4  |  2
%e A303942   18 | 9+9, 9+4+4+1 |  2
%Y A303942 Cf. A011379, A033461, A052335, A303944, A303947.
%K A303942 nonn,look
%O A303942 0,10
%A A303942 _Seiichi Manyama_, May 03 2018