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Search: id:A121677
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| A121677 |
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a(n) = A121676(n)/(n+1) = [x^n] (1 + x*(1+x)^(n-1) )^(n+1) / (n+1). |
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+0
2
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| 1, 1, 2, 8, 50, 402, 3932, 45075, 588450, 8580542, 137799497, 2410575026, 45531000715, 921946835474, 19895218322982, 455271977561120, 11000793881924130, 279648297003419318, 7454931579222301709
(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+1} C(n+1,k) * C((n-1)*k,n-k) / (n+1).
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EXAMPLE
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At n=4, a(4) = [x^4] (1 + x*(1+x)^3 )^5/5 = 250/5 = 50, since
(1 + x*(1+x)^3 )^5 = 1 + 5*x + 25*x^2 + 85*x^3 + 250*x^4 +...
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PROGRAM
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(PARI) a(n)=sum(k=0, n+1, binomial(n+1, k)*binomial((n-1)*k, n-k))/(n+1)
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CROSSREFS
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Cf. A121676; variants: A121673-A121675, A121678-A121680.
Sequence in context: A114619 A027047 A034491 this_sequence A120956 A000557 A002801
Adjacent sequences: A121674 A121675 A121676 this_sequence A121678 A121679 A121680
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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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