A340647 - OEIS

%I #7 Jan 14 2021 11:14:57

%S 1,1,0,2,1,3,2,4,5,6,8,8,14,12,20,18,31,27,42,40,60,60,80,86,111,124,

%T 146,174,199,241,262,328,353,444,464,590,620,780,812,1020,1075,1326,

%U 1400,1710,1833,2198,2370,2804,3072,3570,3936,4522,5048,5713,6414,7190

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

%H Vaclav Kotesovec, <a href="/A340647/b340647.txt">Table of n, a(n) for n = 0..10000</a>

%H Vaclav Kotesovec, <a href="/A340647/a340647.jpg">Graph - the asymptotic ratio</a>

%F a(n) = A006950(n) - A340623(n).

%F a(n) ~ exp(Pi*sqrt(n/2)) / (4*sqrt(2)*n).

%t nmax = 100; CoefficientList[Series[Sum[x^(k^2)/Product[(1-x^(2*j))^2, {j, 1, k}], {k, 0, Sqrt[nmax]}], {x, 0, nmax}], x]

%Y Cf. A000700, A006950, A340623.

%K nonn

%O 0,4

%A _Vaclav Kotesovec_, Jan 14 2021