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Expansion of Sum_{k>=0} x^(k^2) * Product_{j=1..k} (1 + x^j)^j.
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%I #9 Apr 11 2019 09:25:54

%S 1,1,1,0,1,1,2,2,1,2,1,2,5,4,7,9,7,10,9,9,13,13,18,27,31,42,53,61,71,

%T 83,95,98,115,131,147,176,207,258,313,395,481,581,721,848,1014,1179,

%U 1367,1586,1804,2064,2338,2698,3083,3559,4142,4819,5732,6768,8036,9582,11426

%N Expansion of Sum_{k>=0} x^(k^2) * Product_{j=1..k} (1 + x^j)^j.

%H Robert Israel, <a href="/A306911/b306911.txt">Table of n, a(n) for n = 0..4000</a>

%p N:= 100:

%p S:= series(add(x^(k^2)*mul((1+x^j)^j,j=1..min(k,N-k^2)),k=0..floor(sqrt(N))), x, N+1):

%p seq(coeff(S,x,n),n=0..N); # _Robert Israel_, Apr 10 2019

%t nmax = 60; CoefficientList[Series[Sum[x^(k^2) Product[(1 + x^j)^j, {j, 1, k}], {k, 0, nmax}], {x, 0, nmax}], x]

%Y Cf. A306708, A306734, A318771.

%K nonn

%O 0,7

%A _Ilya Gutkovskiy_, Mar 16 2019