A091712 a(n)=6(2n-4)!/((n-2)!n!), if n>2. a(0)=1,a(1)=a(2)=2.

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

Offset

0,2

Links

Table of n, a(n) for n=0..28.

Formula

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.

Prog

(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))

Crossrefs

A007054(n)=a(n+2), if n>0.

Essentially the same as A007054.

Sequence in context: A218694 A143596 A342763 * A125721 A049798 A165198

Adjacent sequences: A091709 A091710 A091711 * A091713 A091714 A091715

Keyword

nonn

Author

Michael Somos, Jan 31 2004

Status

approved