A303944 - OEIS

%I #8 May 03 2018 14:55:18

%S 1,1,1,2,3,4,6,8,11,15,19,25,34,43,55,71,90,113,143,178,222,276,340,

%T 418,515,628,765,931,1128,1362,1643,1974,2369,2836,3385,4033,4800,

%U 5694,6745,7978,9418,11096,13057,15334,17985,21062,24626,28753,33534,39045,45408,52744,61187

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

%F G.f.: Product_{k>=1} (1-x^(k*(k^2+1)))/(1-x^k).

%e   n |                                | a(n)

%e ----+--------------------------------+------

%e   1 | 1                              |  1

%e   2 | 2                              |  1

%e   3 | 3, 2+1                         |  2

%e   4 | 4, 3+1, 2+2                    |  3

%e   5 | 5, 4+1, 3+2, 2+2+1             |  4

%e   6 | 6, 5+1, 4+2, 3+3, 3+2+1, 2+2+2 |  6

%Y Cf. A034262, A052335, A303942.

%K nonn

%O 0,4

%A _Seiichi Manyama_, May 03 2018