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Search: id:A121680
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| A121680 |
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a(n) = [x^n] (1 + x*(1+x)^(n+1) )^(n+1). |
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+0
9
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| 1, 2, 12, 76, 655, 6816, 81690, 1109816, 16782399, 278438740, 5016899833, 97368894756, 2021749249403, 44658312247290, 1044437050070340, 25757381769393392, 667470006331599523, 18119105978249333988
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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) = A121681(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)^5 )^5 = 655, since
(1 + x*(1+x)^5 )^5 = 1 + 5*x + 35*x^2 + 160*x^3 + 655*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. A121681; variants: A121673-A121679.
Sequence in context: A052875 A037725 A037620 this_sequence A081014 A062871 A107632
Adjacent sequences: A121677 A121678 A121679 this_sequence A121681 A121682 A121683
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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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