A211193 E.g.f.: exp((1+x)^(1+x)-1).

1, 1, 3, 10, 45, 221, 1315, 8324, 60809, 464113, 3993811, 35342814, 349085869, 3486862653, 38870528411, 429139127416, 5345350992113, 63994963427393, 887692696733827, 11284513262684914, 175285847038616301, 2298693217837384957, 40805829165456572691

Offset: 0

Author

Robert G. Wilson v, Feb 03 2013

Keywords

• sign

Comments

Note that for odd n >= 31, a(n) is negative! - Vaclav Kotesovec, Feb 13 2013

Conjecture: For n > 1, a(n) == 1 (mod n). - Mélika Tebni, Aug 22 2021

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A000110, A008296.

Programs

Maple

egf:= exp((1+x)^(1+x)-1);
a:= n-> n!*coeff(series(egf, x, n+1), x, n):
seq(a(n), n=0..30);  # Alois P. Heinz, Feb 03 2013
# second program: uses Lehmer-Comtet A008296.
A211193:= n-> add(combinat[bell](k)*A008296(n, k), k=1..n): A211193(0):=1:
seq(A211193(n), n=0..15); # Mélika Tebni, Aug 22 2021

Mathematica

Range[0, 22]! CoefficientList[ Series[ Exp[(1 + x)^(1 + x)], {x, 0, 22}], x]/E

PARI

x='x+O('x^66); Vec(serlaplace(exp((1+x)^(1+x)-1))) \\ Joerg Arndt, Nov 30 2014

Formula

E.g.f.: exp((1+x)^(1+x)-1).

a(n) ~ (n-2)! if n is even and a(n) ~ -(n-2)! if n is odd. - Vaclav Kotesovec, Feb 13 2013

a(n) = Sum_{k=1..n} Bell(k)*A008296(n, k) for n >= 1. - Mélika Tebni, Aug 22 2021