Search: id:A009628
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%I A009628
%S A009628 0,1,2,7,28,141,846,5923,47384,426457,4264570,46910271,562923252,
%T A009628 7318002277,102452031878,1536780478171,24588487650736,418004290062513,
%U A009628 7524077221125234,142957467201379447,2859149344027588940
%V A009628 0,1,-2,7,-28,141,-846,5923,-47384,426457,-4264570,46910271,-562923252,
%W A009628 7318002277,-102452031878,1536780478171,-24588487650736,418004290062513,
%X A009628 -7524077221125234,142957467201379447,-2859149344027588940
%N A009628 Expansion of sinh(x)/(1+x).
%C A009628 (A000166 + A000522)/2 = A009179, (A000166 - A000522)/2 = this_sequence.
%F A009628 a(n) = (-1)^(n+1)*floor(n!*sinh(1)), n>=1. - Vladeta Jovovic (vladeta(AT)eunet.rs), 
               Aug 10 2002
%F A009628 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
%F A009628 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
%F A009628 a(n) = (-1)^n * n! * sum{k=0, [n/2], 1/(2k-1)!}, n>0.
%p A009628 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]
%t A009628 Sinh[x]/(1+x)
%Y A009628 Cf. A051397, A087208.
%Y A009628 Sequence in context: A141318 A030875 A130906 this_sequence A030969 A030825 
               A030897
%Y A009628 Adjacent sequences: A009625 A009626 A009627 this_sequence A009629 A009630 
               A009631
%K A009628 sign,easy
%O A009628 0,3
%A A009628 R. H. Hardin (rhhardin(AT)att.net)
%E A009628 Extended with signs Mar 15 1997 by Olivier Gerard.

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