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Search: id:A009179
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| A009179 |
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Expansion of cosh(x)/(1+x). |
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+0
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; listen)
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OFFSET
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0,3
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COMMENT
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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
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a(n) = (-1)^n*floor(n!*cosh(1)). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Aug 10 2002
a(n)=(1+(-1)^n)/2-n*a(n-1). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Apr 19 2003
a(n) = (-1)^n * n! * sum{k=0, [n/2], 1/(2k)!}.
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MATHEMATICA
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Cosh[ x ]/(1+x)
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CROSSREFS
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Cf. A009628.
Cf. A001540.
Sequence in context: A006229 A008986 A105215 this_sequence A030819 A030904 A030955
Adjacent sequences: A009176 A009177 A009178 this_sequence A009180 A009181 A009182
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KEYWORD
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sign,easy
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AUTHOR
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R. H. Hardin (rhh(AT)cadence.com)
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EXTENSIONS
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Extended with signs Mar 15 1997 by Olivier Gerard.
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