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Search: id:A146559
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| A146559 |
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Expansion of (1-x)/(1-2x+2x^2) . |
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+0
7
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| 1, 1, 0, -2, -4, -4, 0, 8, 16, 16, 0, -32, -64, -64, 0, 128, 256, 256, 0, -512, -1024, -1024, 0, 2048, 4096, 4096, 0, -8192, -16384, -16384, 0, 32768, 65536, 65536, 0, -131072, -262144, -262144, 0, 524288, 1048576, 1048576, 0, -2097152, -4194304
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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Partial sums of this sequence give A099087 . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 01 2008]
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FORMULA
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a(0)=1, a(1)=1, a(n)=2*a(n-1)-2*a(n-2) for n>1 .a(n)=Sum_{k, 0<=k<=n}A124182(n,k)*(-2)^(n-k).
a(n)=Sum_{k, 0<=k<=n}A098158(n,k)*(-1)^(n-k). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 14 2008]
a(n)=(1/2)*[(1-I)^n+(1+I)^n], with n>=0 and I=sqrt(-1) [From Paolo P. Lava (ppl(AT)spl.at), Nov 18 2008]
a(n)=(-1)^n*A009116(n). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 01 2008]
E.g.f.: exp(x)*cos(x) . [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 05 2009]
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MAPLE
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restart: G(x):=exp(x)*cos(x): f[0]:=G(x): for n from 1 to 54 do f[n]:=diff(f[n-1], x) od: x:=0: seq(f[n], n=0..44 ); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 05 2009]
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CROSSREFS
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Cf. A009116
Sequence in context: A111172 A112793 A009116 this_sequence A118434 A090132 A099211
Adjacent sequences: A146556 A146557 A146558 this_sequence A146560 A146561 A146562
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KEYWORD
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sign
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AUTHOR
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Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 01 2008
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