A348088 - OEIS

%I #10 Oct 16 2021 11:05:09

%S 1,1,91,24970,14057043,13444400190,19558289594910,40250341173506100,

%T 111335096965772406915,398473840263173643939190,

%U 1791905773077609090895008106,9890754761467721759394797416396,65747198205879568307026776928408110

%N a(n) = [x^n] Product_{k=1..n} 1/(1 - (2*k-1)^2 * x).

%F a(n) ~ c * d^n * n!^2 / n^(3/2), where d = 52.447924272991536496097233490380538810534457762204101802471270109895148... and c = 0.028365099209561232079163758339093959048662789595134609351298413762... - _Vaclav Kotesovec_, Oct 16 2021

%t Table[SeriesCoefficient[Product[1/(1 - (2*k-1)^2*x), {k, 1, n}], {x, 0, n}], {n, 0, 20}] (* _Vaclav Kotesovec_, Oct 16 2021 *)

%o (PARI) a(n) = polcoef(1/prod(k=1, n, 1-(2*k-1)^2*x+x*O(x^n)), n);

%Y Cf. A001818, A348087.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Sep 28 2021