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Search: id:A121675
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| A121675 |
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a(n) = [x^n] (1 + x*(1+x)^(n+1) )^n. |
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+0
4
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| 1, 1, 7, 43, 371, 3926, 47622, 654151, 9999523, 167557174, 3046387103, 59616689595, 1247357472869, 27747682830531, 653192297754076, 16206706672425167, 422358302959175123, 11526119161103900834
(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)^5 )^4 = 371, since
(1 + x*(1+x)^5 )^4 = 1 + 4*x + 26*x^2 + 104*x^3 + 371*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: A121673, A121674, A121676-A121680.
Sequence in context: A126502 A042213 A127999 this_sequence A023316 A065786 A015463
Adjacent sequences: A121672 A121673 A121674 this_sequence A121676 A121677 A121678
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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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