OFFSET
0,3
COMMENTS
Inverse binomial transform of A194689.
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..555
FORMULA
a(n) ~ 8 * n^(n-3) * exp(n/LambertW(n/2) - n - 2) / (sqrt(1 + LambertW(n/2)) * LambertW(n/2)^(n-3)).
a(0) = 1; a(n) = -3 * a(n-1) + 2 * Sum_{k=1..n} binomial(n-1,k-1) * a(n-k). - Ilya Gutkovskiy, Dec 04 2023
MATHEMATICA
nmax = 30; CoefficientList[Series[Exp[2*Exp[x]-2-3*x], {x, 0, nmax}], x] * Range[0, nmax]!
PROG
(PARI) my(x='x+O('x^30)); Vec(serlaplace(exp(2*(exp(x) - 1) - 3*x))) \\ Michel Marcus, Dec 04 2023
CROSSREFS
KEYWORD
sign
AUTHOR
Vaclav Kotesovec, Jun 26 2022
STATUS
approved