OFFSET
0,4
FORMULA
E.g.f. y(x) satisfies y' = exp(-x)*y^3*x/(1-x)^2.
For all p prime, a(p) == -1 (mod p).
a(n) ~ sqrt(-2*LambertW(-2*exp(-1)/3)/3) * n^n / (exp(n) * (1 + LambertW(-2*exp(-1)/3))^(n+1)). - Vaclav Kotesovec, Jul 01 2021
EXAMPLE
MAPLE
A305404:= n-> add(Stirling2(n, k)*doublefactorial(2*k-1), k=0..n):
A008306 := proc(n, k): if k=1 then (n-1)! ; elif n<=2*k-1 then 0; else (n-1)*procname(n-1, k)+(n-1)*procname(n-2, k-1) ; end if; end proc:
# second program:
a := series(1/sqrt(3-2/((1-x)*exp(x))), x=0, 25):seq(n!*coeff(a, x, n), n=0..24);
MATHEMATICA
CoefficientList[Series[1/Sqrt[3-2/((1-x)*E^x)], {x, 0, 24}], x] * Range[0, 24]!
PROG
(PARI) my(x='x+O('x^30)); Vec(serlaplace(1/sqrt(3 - 2 / ((1 - x)*exp(x))))) \\ Michel Marcus, Jul 01 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Mélika Tebni, Jul 01 2021
STATUS
approved