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A211193
E.g.f.: exp((1+x)^(1+x)-1).
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
0,3
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
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
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
PROG
(PARI) x='x+O('x^66); Vec(serlaplace(exp((1+x)^(1+x)-1))) \\ Joerg Arndt, Nov 30 2014
CROSSREFS
Sequence in context: A096752 A293554 A346066 * A134018 A355719 A028417
KEYWORD
sign
AUTHOR
Robert G. Wilson v, Feb 03 2013
STATUS
approved