%I A009179
%S A009179 1,1,3,9,37,185,1111,7777,62217,559953,5599531,61594841,739138093,
%T A009179 9608795209,134523132927,2017846993905,32285551902481,548854382342177,
%U A009179 9879378882159187,187708198761024553,3754163975220491061
%V A009179 1,-1,3,-9,37,-185,1111,-7777,62217,-559953,5599531,-61594841,739138093,
%W A009179 -9608795209,134523132927,-2017846993905,32285551902481,-548854382342177,
%X A009179 9879378882159187,-187708198761024553,3754163975220491061
%N A009179 Expansion of cosh(x)/(1+x).
%C A009179 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
%C A009179 (A000166 + A000522)/2 = this_sequence, (A000166 - A000522)/2 = A009628.
%C A009179 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
%F A009179 a(n) = (-1)^n*floor(n!*cosh(1)). - Vladeta Jovovic (vladeta(AT)eunet.rs), 
               Aug 10 2002
%F A009179 a(n)=(1+(-1)^n)/2-n*a(n-1). - Vladeta Jovovic (vladeta(AT)eunet.rs), 
               Apr 19 2003
%F A009179 a(n) = (-1)^n * n! * sum{k=0, [n/2], 1/(2k)!}.
%F A009179 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]
%p A009179 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]
%t A009179 Cosh[ x ]/(1+x)
%Y A009179 Cf. A009628.
%Y A009179 Cf. A001540.
%Y A009179 Sequence in context: A008986 A105215 A158053 this_sequence A030819 A030904 
               A030955
%Y A009179 Adjacent sequences: A009176 A009177 A009178 this_sequence A009180 A009181 
               A009182
%K A009179 sign,easy
%O A009179 0,3
%A A009179 R. H. Hardin (rhhardin(AT)att.net)
%E A009179 Extended with signs Mar 15 1997 by Olivier Gerard.