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Search: id:A009628
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| A009628 |
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Expansion of sinh(x)/(1+x). |
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+0
5
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| 0, 1, -2, 7, -28, 141, -846, 5923, -47384, 426457, -4264570, 46910271, -562923252, 7318002277, -102452031878, 1536780478171, -24588487650736, 418004290062513, -7524077221125234, 142957467201379447, -2859149344027588940
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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(A000166 + A000522)/2 = A009179, (A000166 - A000522)/2 = this_sequence.
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FORMULA
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a(n) = (-1)^(n+1)*floor(n!*sinh(1)), n>=1. - Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 10 2002
Let u(1)=1, u(n)=n*u(n-1)+n (mod 2); then for n>0, a(n)=(-1)^(n+1)*u(n) - Benoit Cloitre (benoit7848c(AT)orange.fr), Jan 12 2003
Unsigned sequence satisfies a(n)=na(n-1)+a(n-2)-(n-2)a(n-3), with E.g.f. sinh(z)/(1-z) - Mario Catalani (mario.catalani(AT)unito.it), Feb 08 2003
a(n) = (-1)^n * n! * sum{k=0, [n/2], 1/(2k-1)!}, n>0.
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MAPLE
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restart: G(x):= sinh(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
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Sinh[x]/(1+x)
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CROSSREFS
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Cf. A051397, A087208.
Sequence in context: A141318 A030875 A130906 this_sequence A030969 A030825 A030897
Adjacent sequences: A009625 A009626 A009627 this_sequence A009629 A009630 A009631
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KEYWORD
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sign,easy
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AUTHOR
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R. H. Hardin (rhhardin(AT)att.net)
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EXTENSIONS
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Extended with signs Mar 15 1997 by Olivier Gerard.
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