OFFSET
0,4
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..440
FORMULA
a(0) = 1; a(n) = Sum_{k=1..n} (k! - 1) * binomial(n-1,k-1) * a(n-k).
a(n) ~ exp(1/2 - exp(1) + 2*sqrt(n) - n) * n^(n - 1/4) / sqrt(2). - Vaclav Kotesovec, Jul 21 2022
MATHEMATICA
nmax = 20; CoefficientList[Series[E^(1/(1-x) - E^x), {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Jul 21 2022 *)
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(1/(1-x)-exp(x))))
(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, (j!-1)*binomial(i-1, j-1)*v[i-j+1])); v;
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jul 14 2022
STATUS
approved