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A110609
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n * C(2*n,n-1).
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1
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0, 1, 8, 45, 224, 1050, 4752, 21021, 91520, 393822, 1679600, 7113106, 29953728, 125550100, 524190240, 2181340125, 9051563520, 37467344310, 154754938800, 637982011590, 2625648168000, 10789623755820, 44277560801760
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Second column of number triangle A110608.
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FORMULA
| a(n) = n^2*binomial(2*n, n)/(n+1) = n^2*A000108(n) = A002736(n)/(n+1).
G.f.: -((2*x*(2*x+2*sqrt(1-4*x)-3) - sqrt(1-4*x) + 1)/(2*sqrt((1 - 4*x)^3)* x^2)). [From Marco A. Cisneros Guevara, July 23 2011]
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MAPLE
| with(combinat):with(combstruct):a[0]:=0:for n from 1 to 30 do a[n]:=sum((count(Composition(n*2+1), size=n)), j=1..n) od: seq(a[n], n=0..22); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 09 2007
a:=n->sum(sum(binomial(2*n, n)/(n+1), j=1..n), k=1..n): seq(a(n), n=0..22); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 09 2007
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MATHEMATICA
| Table[CatalanNumber[n]*n^2, {n, 0, 22}] [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 08 2009]
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CROSSREFS
| Sequence in context: A002696 A016208 A026852 * A201190 A032208 A163003
Adjacent sequences: A110606 A110607 A110608 * A110610 A110611 A110612
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Jul 30 2005
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