A356559 a(n) = exp(-1) * n! * Sum_{k>=0} Laguerre(n,k) / k!.

1, 0, 0, 1, 7, 43, 281, 2056, 17004, 157809, 1622515, 18245335, 222004597, 2898508416, 40343356184, 595578837205, 9287308741827, 152459628788599, 2627373030049669, 47425289731038656, 895098852673047772, 17644305594671247141, 363065584549610882703, 7799894520723959486795

Offset

0,5

Links

Table of n, a(n) for n=0..23.

Eric Weisstein's World of Mathematics, Laguerre Polynomial

Formula

E.g.f.: exp(exp(-x/(1 - x)) - 1) / (1 - x).

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

Mathematica

Table[Exp[-1] n! Sum[LaguerreL[n, k]/k!, {k, 0, Infinity}], {n, 0, 23}]
nmax = 23; CoefficientList[Series[Exp[Exp[-x/(1 - x)] - 1]/(1 - x), {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[(-1)^(n - k) Binomial[n, k]^2 k! BellB[n - k], {k, 0, n}], {n, 0, 23}]

Prog

(PARI) my(x='x+O('x^30)); Vec(serlaplace(exp(exp(-x/(1 - x)) - 1) / (1 - x))) \\ Michel Marcus, Aug 12 2022

Crossrefs

Cf. A000110, A009940, A101053, A317362, A317366.

Sequence in context: A286911 A343351 A277188 * A351757 A338675 A244938

Adjacent sequences: A356556 A356557 A356558 * A356560 A356561 A356562

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 12 2022

Status

approved