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Search: id:A085373
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| A085373 |
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a(n)=C(2n+1,n+1)C(n+2,2). |
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+0
4
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| 1, 9, 60, 350, 1890, 9702, 48048, 231660, 1093950, 5080790, 23279256, 105462084, 473227300, 2106121500, 9307051200, 40873466520, 178520875830, 775924068150, 3357800061000, 14473885526100, 62168784497820, 266168518910580
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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a(n)= A119578(n+1)/2 - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 19 2008
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FORMULA
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a(n-1)=sum(i1+i2+...+in) where the sum is over 1<=i1<=i2<=...<=in<=n. G.f.: (1 - x)/(1 - 4x)^(5/2) - David Callan (callan(AT)stat.wisc.edu), Nov 20 2003
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MAPLE
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a:=n->sum(j, j=1..n)*binomial(2*n, n)/2: seq(a(n), n=1..22); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 08 2007
a:=n->sum((n+j)*binomial(2*n, n)/3!, j=0..n): seq(a(n), n=1..22); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 08 2007
a:=n->sum(sum(binomial(2*n, n)/4, j=1..n), k=0..n): seq(a(n), n=1..22); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 08 2007
with (combinat):seq (stirling2(n+1, n)*binomial(2*n, n)/2, n=1..22); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 19 2008
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MATHEMATICA
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Table[Binomial[2 n + 1, n + 1]Binomial[n + 2, 2], {n, 0, 30}]
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PROGRAM
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(PARI) a(n)=binomial(2*n+1, n+1)*binomial(n+2, 2)
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CROSSREFS
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Cf. A002544.
Cf. A000984.
Sequence in context: A118674 A074431 A081904 this_sequence A082150 A026785 A153820
Adjacent sequences: A085370 A085371 A085372 this_sequence A085374 A085375 A085376
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KEYWORD
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easy,nonn
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AUTHOR
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Mario Catalani (mario.catalani(AT)unito.it), Jun 26 2003
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