A376712 - OEIS

%I #5 Oct 02 2024 12:30:56

%S 1,1,4,10,21,39,70,120,205,342,568,924,1490,2356,3684,5666,8619,12935,

%T 19230,28280,41260,59680,85740,122306,173447,244472,342774,478014,

%U 663391,916149,1259526,1723772,2349209,3188160,4309660,5803002,7785040,10406296,13862404

%N G.f.: Sum_{k>=0} x^(k^2) * Product_{j=1..k} 1/(1 - x^j)^4.

%F a(n) ~ exp(2*Pi*sqrt(2*n/5)) / (5^(5/4) * (sqrt(5)-1)^2 * n^(3/2)).

%t nmax = 40; CoefficientList[Series[Sum[x^(k^2)/Product[1-x^j, {j, 1, k}]^4, {k, 0, Sqrt[nmax]}], {x, 0, nmax}], x]

%Y Cf. A003114, A000041, A376709.

%K nonn

%O 0,3

%A _Vaclav Kotesovec_, Oct 02 2024