A348088 a(n) = [x^n] Product_{k=1..n} 1/(1 - (2*k-1)^2 * x).

1, 1, 91, 24970, 14057043, 13444400190, 19558289594910, 40250341173506100, 111335096965772406915, 398473840263173643939190, 1791905773077609090895008106, 9890754761467721759394797416396, 65747198205879568307026776928408110

Offset

0,3

Links

Table of n, a(n) for n=0..12.

Formula

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

Mathematica

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

Prog

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

Crossrefs

Cf. A001818, A348087.

Sequence in context: A319370 A116507 A083828 * A157802 A214110 A119130

Adjacent sequences: A348085 A348086 A348087 * A348089 A348090 A348091

Keyword

nonn

Author

Seiichi Manyama, Sep 28 2021

Status

approved