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Search: id:A121673
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| A121673 |
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a(n) = [x^n] (1 + x*(1+x)^(n-1) )^n. |
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+0
9
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| 1, 1, 3, 16, 131, 1306, 15257, 203967, 3047907, 50115310, 896746169, 17308420306, 357767229778, 7872926416538, 183537476164902, 4513828442107368, 116688468769638435, 3160881019508153238, 89471871451166037425
(list; graph; listen)
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OFFSET
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0,3
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FORMULA
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a(n) = Sum_{k=0..n} C(n,k) * C((n-1)*k,n-k).
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EXAMPLE
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At n=4, a(4) = [x^4] (1 + x*(1+x)^3 )^4 = 131, since
(1 + x*(1+x)^3 )^4 = 1 + 4*x + 18*x^2 + 52*x^3 + 131*x^4 +...
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PROGRAM
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(PARI) a(n)=sum(k=0, n, binomial(n, k)*binomial((n-1)*k, n-k))
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CROSSREFS
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Cf. variants: A121674-A121680.
Adjacent sequences: A121670 A121671 A121672 this_sequence A121674 A121675 A121676
Sequence in context: A135752 A120021 A131490 this_sequence A051921 A023998 A141628
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Aug 15 2006
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