A354437 a(n) = n! * Sum_{k=0..n} (-k)^(n-k)/k!.

1, 1, -1, 1, 13, -199, 2251, -19991, 7001, 7530193, -330734249, 11005284401, -300961551131, 4886902605001, 184195977487523, -28517140157423399, 2322376314679777201, -153646291657993064671, 8388000381774954552751, -287686436757241322569247

Offset: 0

Author

Seiichi Manyama, May 28 2022

Keywords

• sign

Crossrefs

Cf. A038125, A277509, A354436.

Programs

Mathematica

Join[{1}, Table[n!*Sum[ (-k)^(n - k)/k!, {k, 0, n}], {n, 1, 20}]] (* Vaclav Kotesovec, May 28 2022 *)

PARI

a(n) = n!*sum(k=0, n, (-k)^(n-k)/k!);

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, x^k/(k!*(1+k*x)))))

Python

from math import factorial
def A354437(n): return sum(factorial(n)*(-k)**(n-k)//factorial(k) for k in range(n+1)) # Chai Wah Wu, May 28 2022

Formula

E.g.f.: Sum_{k>=0} x^k / (k! * (1 + k*x)).