0,3

Unsigned sequence satisfies a(n)=na(n-1)+a(n-2)-(n-2)a(n-3), a(0)=1,a(1)=1,a(2)=3 with E.g.f. Cosh(z)/(1-z). - Mario Catalani (mario.catalani(AT)unito.it), Feb 07 2003

(A000166 + A000522)/2 = this_sequence, (A000166 - A000522)/2 = A009628.

The positive sequence has e.g.f. cosh(x)/(1-x), with a(n)=sum{k=0..floor(n/2), binomial(n,2k)(n-2k)!}. It is the mean of the binomial and inverse binomial transforms of n!. - Paul Barry (pbarry(AT)wit.ie), May 01 2005

a(n) = (-1)^n*floor(n!*cosh(1)). - Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 10 2002

a(n)=(1+(-1)^n)/2-n*a(n-1). - Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 19 2003

a(n) = (-1)^n * n! * sum{k=0, [n/2], 1/(2k)!}.

a(n)=[n!*(-1)^n]*{1+(1/2)*{Sum[k=1..n][1/k! ]+Sum[j=1..n][(1/j!)*(-1)^j]}}, with n>=0 [From Paolo P. Lava (ppl(AT)spl.at), Jan 14 2009]

restart: G(x):= cosh(x)/(1+x): f[0]:=G(x): for n from 1 to 21 do f[n]:=diff(f[n-1], x) od: x:=0: seq(f[n], n=0..20); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 03 2009]

Cosh[ x ]/(1+x)

Cf. A009628.

Cf. A001540.

Sequence in context: A008986 A105215 A158053 this_sequence A030819 A030904 A030955

Adjacent sequences: A009176 A009177 A009178 this_sequence A009180 A009181 A009182

sign,easy

R. H. Hardin (rhhardin(AT)att.net)

Extended with signs Mar 15 1997 by Olivier Gerard.