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%I #11 Mar 14 2013 15:01:08
%S 1,1,2,1,1,2,3,4,3,3,3,3,6,7,8,10,9,9,9,9,11,13,16,20,22,25,28,27,28,
%T 29,30,32,35,40,45,53,60,67,73,79,85,87,92,95,98,105,111,120,132,145,
%U 160,178,196,212,231,247,263,280,291,305,319,334,352
%N Counting a set of restricted partitions
%F G.f.: sum(k>=0, x^(k^2) * prod(j=1..k, (1+x^j)^2 ) ) = 1 +x^1*(1+x)^2 +x^4*(1+x)^2*(1+x^2)^2 +...+ x^k^2*(1+x)^2*(1+x^2)^2*(1+x^3)^2*...*(1+x^k)^2+...
%t Take[CoefficientList[Sum[x^(k^2)*Product[1 + x^i, {i, k}]^2, {k, 0, 7}], x], 63] (* _Giovanni Resta_, Mar 13 2013 *)
%K nonn
%O 0,3
%A _David S. Newman_, Mar 13 2013
%E a(14)-a(62) from _Giovanni Resta_, Mar 13 2013
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