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A009179
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Expansion of cosh(x)/(1+x).
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6
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1, -1, 3, -9, 37, -185, 1111, -7777, 62217, -559953, 5599531, -61594841, 739138093, -9608795209, 134523132927, -2017846993905, 32285551902481, -548854382342177, 9879378882159187, -187708198761024553, 3754163975220491061
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| 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
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FORMULA
| 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 (paoloplava(AT)gmail.com), Jan 14 2009]
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MAPLE
| 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]
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MATHEMATICA
| Cosh[ x ]/(1+x)
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CROSSREFS
| Cf. A009628.
Cf. A001540.
Sequence in context: A008986 A105215 A158053 * A030819 A030904 A030955
Adjacent sequences: A009176 A009177 A009178 * A009180 A009181 A009182
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KEYWORD
| sign,easy
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AUTHOR
| R. H. Hardin (rhhardin(AT)att.net)
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EXTENSIONS
| Extended with signs Mar 15 1997 by Olivier Gerard.
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