OFFSET
0,5
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..593
FORMULA
a(n) = exp(1) * Sum_{k>=0} (-1)^k*(k + 1)^n/k!. - Ilya Gutkovskiy, Jun 13 2019
a(n) = Sum_{k=0..n} binomial(n,k) * Bell(k, -1). - Vaclav Kotesovec, Jul 06 2020
a(0) = 1; a(n) = - Sum_{k=0..n-2} binomial(n-1,k) * a(k). - Seiichi Manyama, Aug 02 2021
MAPLE
f:= series(exp(1 + x - exp(x)), x= 0, 101): seq(factorial(n) * coeff(f, x, n), n = 0..30); # Muniru A Asiru, Oct 31 2017
# second Maple program:
b:= proc(n, t) option remember; `if`(n=0, 1-2*t,
add(b(n-j, 1-t)*binomial(n-1, j-1), j=1..n))
end:
a:= n-> b(n+1, 1):
seq(a(n), n=0..35); # Alois P. Heinz, Dec 01 2021
MATHEMATICA
m = 26; Range[0, m]! * CoefficientList[Series[Exp[1 + x - Exp[x]], {x, 0, m}], x] (* Amiram Eldar, Jul 06 2020 *)
Table[Sum[Binomial[n, k] * BellB[k, -1], {k, 0, n}], {n, 0, 30}] (* Vaclav Kotesovec, Jul 06 2020 *)
PROG
(PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(-exp(x)+1+x)))
(PARI) a(n) = if(n==0, 1, -sum(k=0, n-2, binomial(n-1, k)*a(k))); \\ Seiichi Manyama, Aug 02 2021
KEYWORD
sign
AUTHOR
Seiichi Manyama, Sep 28 2017
STATUS
approved