cp's OEIS Frontend

A303944 Number of partitions of n into at most 1^2 copy of 1, 2^2 copies of 2, 3^2 copies of 3, ... .

%I A303944 #8 May 03 2018 14:55:18
%S A303944 1,1,1,2,3,4,6,8,11,15,19,25,34,43,55,71,90,113,143,178,222,276,340,
%T A303944 418,515,628,765,931,1128,1362,1643,1974,2369,2836,3385,4033,4800,
%U A303944 5694,6745,7978,9418,11096,13057,15334,17985,21062,24626,28753,33534,39045,45408,52744,61187
%N A303944 Number of partitions of n into at most 1^2 copy of 1, 2^2 copies of 2, 3^2 copies of 3, ... .
%F A303944 G.f.: Product_{k>=1} (1-x^(k*(k^2+1)))/(1-x^k).
%e A303944   n |                                | a(n)
%e A303944 ----+--------------------------------+------
%e A303944   1 | 1                              |  1
%e A303944   2 | 2                              |  1
%e A303944   3 | 3, 2+1                         |  2
%e A303944   4 | 4, 3+1, 2+2                    |  3
%e A303944   5 | 5, 4+1, 3+2, 2+2+1             |  4
%e A303944   6 | 6, 5+1, 4+2, 3+3, 3+2+1, 2+2+2 |  6
%Y A303944 Cf. A034262, A052335, A303942.
%K A303944 nonn
%O A303944 0,4
%A A303944 _Seiichi Manyama_, May 03 2018