A282866 - OEIS

%I #8 Mar 15 2017 20:26:51

%S 1,1,0,0,4,4,0,0,0,9,9,0,0,36,36,0,16,16,0,0,64,64,0,0,0,169,169,0,0,

%T 676,676,0,0,0,225,225,36,36,900,900,144,544,400,0,0,1924,1924,0,0,

%U 1345,4945,3600,576,772,14596,14400,2304,2304,441,441,0,6084,7848,1764,64,25184,25120,0,256,3392,11236,8100,0,576

%N Expansion of Product_{k>=1} (1 + k^2*x^(k^2)).

%C Sum of products of terms in all partitions of n into distinct squares (A000290).

%H <a href="/index/Par#partN">Index entries for related partition-counting sequences</a>

%H <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>

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

%e a(41) = 544 because we have [36, 4, 1], [25, 16], 36*4*1 = 144, 25*16 = 400 and 144 + 400 = 544.

%t nmax = 73; CoefficientList[Series[Product[1 + k^2 x^k^2, {k, 1, nmax}], {x, 0, nmax}], x]

%o (PARI) Vec(prod(k=1, 73, (1 + k^2*x^(k^2))) + O(x^73)) \\ _Indranil Ghosh_, Mar 15 2017

%Y Cf. A000290, A022629, A033461, A282209.

%K nonn

%O 0,5

%A _Ilya Gutkovskiy_, Feb 23 2017