A348087 a(n) = [x^n] Product_{k=1..n} 1/(1 - (2*k-1) * x).

1, 1, 13, 330, 12411, 618870, 38461522, 2863440580, 248440887123, 24616763946918, 2742625188929990, 339386813915985836, 46184075261030623710, 6854605372617955658940, 1101943692701420653738500, 190748265085183804327197000, 35373318817392757170821576835

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..317

Formula

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

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

a(n) ~ 2^(3*n - 1) * n^(n - 1/2) / (sqrt(Pi*(1-c)) * (2-c)^n * c^(n - 1/2) * exp(n)), where c = -LambertW(-2*exp(-2)) = -A226775 = 0.4063757399599599... - Vaclav Kotesovec, Oct 02 2021

Prog

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

Crossrefs

Cf. A001147, A007820, A039755, A348085, A348088.

Sequence in context: A296395 A183440 A296018 * A142543 A258297 A266902

Adjacent sequences: A348084 A348085 A348086 * A348088 A348089 A348090

Keyword

nonn

Author

Seiichi Manyama, Sep 28 2021

Status

approved