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Search: id:A121676
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| A121676 |
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a(n) = [x^n] (1 + x*(1+x)^(n-1) )^(n+1). |
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+0
5
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| 1, 2, 6, 32, 250, 2412, 27524, 360600, 5296050, 85805420, 1515794467, 28926900312, 591903009295, 12907255696636, 298428274844730, 7284351640977920, 187013495992710210, 5033669346061547724, 141643700005223732471
(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) is divisible by (n+1): a(n)/(n+1) = A121677(n).
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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).
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EXAMPLE
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At n=4, a(4) = [x^4] (1 + x*(1+x)^3 )^5 = 250, 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))
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CROSSREFS
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Cf. A121677; variants: A121673-A121675, A121678-A121680.
Adjacent sequences: A121673 A121674 A121675 this_sequence A121677 A121678 A121679
Sequence in context: A012318 A012521 A012324 this_sequence A133596 A088437 A005736
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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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