A281790 - OEIS

%I #19 Aug 28 2018 13:08:08

%S 1,1,0,0,2,2,0,0,1,4,3,0,0,6,6,0,4,7,6,3,8,8,6,6,4,21,20,4,1,34,34,2,

%T 8,23,44,28,19,18,54,54,18,56,65,46,25,100,94,38,42,85,169,107,56,69,

%U 226,194,62,111,194,241,125,215,246,258,207,283,437,292

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

%H Vaclav Kotesovec, <a href="/A281790/b281790.txt">Table of n, a(n) for n = 0..20000</a>

%F a(n) ~ exp(sqrt(n/6)*Pi) / (2^(11/6) * 3^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Apr 15 2017

%t nmax = 100; CoefficientList[Series[Product[(1+x^(k^2))^k, {k,1,nmax}], {x,0,nmax}], x]

%t nmax = 100; s = 1 + x; Do[s*=Sum[Binomial[k, j]*x^(j*k^2), {j, 0, Floor[nmax/k^2] + 1}]; s = Select[Expand[s], Exponent[#, x] <= nmax &];, {k, 2, nmax}]; CoefficientList[s, x]

%Y Cf. A000219, A026007, A027998, A033461, A255528, A266891, A284896, A285047.

%K nonn

%O 0,5

%A _Vaclav Kotesovec_, Apr 14 2017