OFFSET
0,4
FORMULA
a(n) = n! * [x^n] exp(-x/(1 - n*x)) / (1 - n*x).
a(n) = Sum_{k=0..n} (-1)^(n - k) * binomial(n,k)^2 * n^k * k!.
a(n) ~ sqrt(2*Pi) * BesselJ(0,2) * n^(2*n + 1/2) / exp(n). - Vaclav Kotesovec, Dec 18 2019
MATHEMATICA
Join[{1}, Table[n! Sum[(-1)^k Binomial[n, k] n^(n - k)/k!, {k, 0, n}], {n, 1, 15}]]
Join[{1}, Table[n^n n! LaguerreL[n, 1/n], {n, 1, 15}]]
Table[n! SeriesCoefficient[Exp[-x/(1 - n x)]/(1 - n x), {x, 0, n}], {n, 0, 15}]
PROG
(Magma) [Factorial(n)*&+[(-1)^k*Binomial(n, k)*n^(n-k)/Factorial(k):k in [0..n]]:n in [0..15]]; // Marius A. Burtea, Dec 18 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 18 2019
STATUS
approved