%I #9 Feb 04 2024 09:00:41

%S 1,1,5,14,34,95,208,537,1090,2812,5566,12480,26199,53486,112866,

%T 229111,450800,885030,1778190,3319846,6624376,12354288,23674929,

%U 43485580,81441398,149864634,273431081,503205344,906757150,1630802024,2920280596,5166820832

%N Sum of products of squares of parts , counted without multiplicity, in all partitions of n.

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

%e The partitions of 4 are 4, 3+1, 2+2, 2+1+1, 1+1+1+1. So a(4) = 16 + 9 + 4 + 4 + 1 = 34.

%o (PARI) my(N=40, x='x+O('x^N)); Vec(prod(k=1, N, 1+k^2*x^k/(1-x^k)))

%Y Cf. A162506, A369888.

%Y Cf. A077335.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Feb 04 2024