A348084 a(n) = [x^n] Product_{k=1..2*n} 1/(1 - k * x).

1, 3, 65, 2646, 159027, 12662650, 1256328866, 149304004500, 20677182465555, 3270191625210510, 581535955088511150, 114860168436414644100, 24947615188488584876910, 5909902157669174347277556, 1516413100622001261250104100, 418965782063742792530650053000

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..300

Formula

a(n) = S2(3*n,2*n), where S2(n,k) is Stirling numbers of the second kind.

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

a(n) ~ 3^(3*n) * n^(n - 1/2) / (sqrt(Pi*(1-c)) * 2^(n+1) * exp(n) * (3 - 2*c)^n * c^(2*n)), where c = -LambertW(-3*exp(-3/2)/2) = 0.62578253420128292093838... - Vaclav Kotesovec, Oct 02 2021

Prog

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

Crossrefs

Cf. A007820 (S2(2*n,n)), A008277 (S2(n,k)), A129505, A348085.

Sequence in context: A216859 A346162 A012804 * A012837 A036778 A295169

Adjacent sequences: A348081 A348082 A348083 * A348085 A348086 A348087

Keyword

nonn

Author

Seiichi Manyama, Sep 28 2021

Status

approved