cp's OEIS Frontend

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

%I A211193 #47 Aug 23 2021 03:38:17
%S A211193 1,1,3,10,45,221,1315,8324,60809,464113,3993811,35342814,349085869,
%T A211193 3486862653,38870528411,429139127416,5345350992113,63994963427393,
%U A211193 887692696733827,11284513262684914,175285847038616301,2298693217837384957,40805829165456572691
%N A211193 E.g.f.: exp((1+x)^(1+x)-1).
%C A211193 Note that for odd n >= 31, a(n) is negative! - _Vaclav Kotesovec_, Feb 13 2013
%C A211193 Conjecture: For n > 1, a(n) == 1 (mod n). - _Mélika Tebni_, Aug 22 2021
%H A211193 Alois P. Heinz, <a href="/A211193/b211193.txt">Table of n, a(n) for n = 0..200</a>
%F A211193 E.g.f.: exp((1+x)^(1+x)-1).
%F A211193 a(n) ~ (n-2)! if n is even and a(n) ~ -(n-2)! if n is odd. - _Vaclav Kotesovec_, Feb 13 2013
%F A211193 a(n) = Sum_{k=1..n} Bell(k)*A008296(n, k) for n >= 1. - _Mélika Tebni_, Aug 22 2021
%p A211193 egf:= exp((1+x)^(1+x)-1);
%p A211193 a:= n-> n!*coeff(series(egf, x, n+1), x, n):
%p A211193 seq(a(n), n=0..30);  # _Alois P. Heinz_, Feb 03 2013
%p A211193 # second program: uses Lehmer-Comtet A008296.
%p A211193 A211193:= n-> add(combinat[bell](k)*A008296(n, k), k=1..n): A211193(0):=1:
%p A211193 seq(A211193(n), n=0..15); # _Mélika Tebni_, Aug 22 2021
%t A211193 Range[0, 22]! CoefficientList[ Series[ Exp[(1 + x)^(1 + x)], {x, 0, 22}], x]/E
%o A211193 (PARI) x='x+O('x^66); Vec(serlaplace(exp((1+x)^(1+x)-1))) \\ _Joerg Arndt_, Nov 30 2014
%Y A211193 Cf. A000110, A008296.
%K A211193 sign
%O A211193 0,3
%A A211193 _Robert G. Wilson v_, Feb 03 2013