A348085 a(n) = [x^n] Product_{k=1..2*n} 1/(1 - (2*k-1) * x).

1, 4, 170, 13776, 1652442, 262842580, 52116296024, 12380577235040, 3427841258566890, 1083931844930932140, 385417972804020879450, 152219732613102667656000, 66113646914860527721527960, 31319437721634527178263452656

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..277

Formula

a(n) = A039755(3*n-1,2*n-1) for n > 0.

a(n) = (-1/(2^(2*n-1) * (2*n-1)!)) * Sum_{k=0..2*n-1} (-1)^k * (2*k+1)^(3*n-1) * binomial(2*n-1,k) for n > 0.

a(n) ~ 3^(3*n - 1/2) * n^(n - 1/2) / (sqrt(2*Pi*(1-c)) * (3 - 2*c)^n * c^(2*n - 1/2) * exp(n)), where c = -LambertW(-3*exp(-3/2)/2) = 0.62578253420128292... - Vaclav Kotesovec, Oct 02 2021

Prog

(PARI) a(n) = polcoef(1/prod(k=1, 2*n, 1-(2*k-1)*x+x*O(x^n)), n);
(PARI) a(n) = if(n==0, 1, -sum(k=0, 2*n-1, (-1)^k*(2*k+1)^(3*n-1)*binomial(2*n-1, k))/(2^(2*n-1)*(2*n-1)!));

Crossrefs

Cf. A039755, A293318, A348082, A348084, A348087.

Sequence in context: A306402 A057140 A245323 * A195631 A145245 A081783

Adjacent sequences: A348082 A348083 A348084 * A348086 A348087 A348088

Keyword

nonn

Author

Seiichi Manyama, Sep 28 2021

Status

approved