cp's OEIS Frontend

A350249 a(n) is the constant term in expansion of Product_{k=1..n} (x^(k^2) + 1 + 1/x^(k^2)).

%I A350249 #19 Feb 05 2022 02:29:59
%S A350249 1,1,1,1,1,3,7,19,43,95,189,429,1003,2457,6319,16165,41601,107969,
%T A350249 280253,737065,1950865,5201941,13954313,37593679,101695957,276296549,
%U A350249 753191093,2061201397,5658850121,15583938539,43040609115,119182143639,330841253283,920550527585
%N A350249 a(n) is the constant term in expansion of Product_{k=1..n} (x^(k^2) + 1 + 1/x^(k^2)).
%H A350249 Vaclav Kotesovec, <a href="/A350249/b350249.txt">Table of n, a(n) for n = 0..200</a>
%F A350249 Conjecture: a(n) ~ sqrt(5) * 3^(n + 1/2) / (2*sqrt(Pi)*n^(5/2)). - _Vaclav Kotesovec_, Feb 04 2022
%p A350249 b:= proc(n) option remember; `if`(n=0, 1,
%p A350249       expand((x^(n^2)+1+1/x^(n^2))*b(n-1)))
%p A350249     end:
%p A350249 a:= n-> coeff(b(n),x,0):
%p A350249 seq(a(n), n=0..33);  # _Alois P. Heinz_, Jan 28 2022
%t A350249 Table[Coefficient[Product[x^(k^2) + 1 + 1/x^(k^2), {k, 1, n}], x, 0], {n, 0, 30}] (* _Vaclav Kotesovec_, Feb 05 2022 *)
%Y A350249 Cf. A007576, A158092, A350495, A350880.
%K A350249 nonn
%O A350249 0,6
%A A350249 _Ilya Gutkovskiy_, Jan 28 2022