A355575 a(n) = n! * Sum_{k=0..floor(n/3)} k^(n - 3*k)/k!.

1, 0, 0, 6, 24, 120, 1080, 10080, 120960, 1874880, 34473600, 738460800, 17982518400, 489858969600, 14834839219200, 498452777222400, 18583796335104000, 768773914900992000, 35220800475250790400, 1779227869201400217600, 98469904378626772992000

Offset

0,4

Links

Seiichi Manyama, Table of n, a(n) for n = 0..323

Formula

E.g.f.: Sum_{k>=0} x^(3*k) / (k! * (1 - k * x)).

a(n) ~ sqrt(Pi) * exp((n - 1/2)/LambertW(exp(3/4)*(2*n - 1)/8) - 2*n) * n^(2*n + 1/2) / (sqrt(1 + LambertW(exp(3/4)*(2*n - 1)/8)) * 2^(2*n + 1/2) * LambertW(exp(3/4)*(2*n - 1)/8)^n). - Vaclav Kotesovec, Oct 30 2022

Mathematica

Join[{1}, Table[n!*Sum[k^(n - 3*k)/k!, {k, 0, n/3}], {n, 1, 20}]] (* Vaclav Kotesovec, Oct 30 2022 *)

Prog

(PARI) a(n) = n!*sum(k=0, n\3, k^(n-3*k)/k!);
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, x^(3*k)/(k!*(1-k*x)))))

Crossrefs

Cf. A345747, A354436.

Cf. A292889, A352945.

Sequence in context: A182083 A293049 A293123 * A060249 A052557 A357192

Adjacent sequences: A355572 A355573 A355574 * A355576 A355577 A355578

Keyword

nonn

Author

Seiichi Manyama, Sep 17 2022

Status

approved