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Search: id:A091712
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| A091712 |
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a(n)=6(2n-4)!/((n-2)!n!), if n>2. a(0)=1,a(1)=a(2)=2. |
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2
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| 1, 2, 2, 2, 3, 6, 14, 36, 99, 286, 858, 2652, 8398, 27132, 89148, 297160, 1002915, 3421710, 11785890, 40940460, 143291610, 504932340, 1790214660, 6382504440, 22870640910, 82334307276, 297670187844, 1080432533656, 3935861372604
(list; graph; listen)
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OFFSET
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0,2
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FORMULA
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G.f.: ((1+10x-2x^2)+(1-4x)^(3/2))/2. a(n)=6(2n-4)!/((n-2)!n!), if n>2. a(n)=a(n-1)(4n-10)/n, if n>3.
G.f. A(x) = (2c(x)-1)^3/c(x)^4 = (1-c(x)x)(1+c(x)x)^3, where c(x) = g.f. for Catalan numbers A000108.
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PROGRAM
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(PARI) a(n)=if(n<3, (n>=0)+(n>0), 6*(2*n-4)!/n!/(n-2)!)
(PARI) a(n)=if(n<0, 0, polcoeff(((1+10*x-2*x^2)+(1-4*x)*sqrt(1-4*x+x*O(x^n)))/2, n))
(PARI) a(n)=if(n<=0, n==0, polcoeff(subst((1-x)*(1+x)^3, x, serreverse(x-x^2+x*O(x^n))), n))
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CROSSREFS
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A007054(n)=a(n+2), if n>0.
Essentially the same as A007054.
Sequence in context: A096235 A147851 A143596 this_sequence A125721 A049798 A165198
Adjacent sequences: A091709 A091710 A091711 this_sequence A091713 A091714 A091715
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Jan 31 2004
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