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Search: id:A121674
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| A121674 |
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a(n) = [x^n] (1 + x*(1+x)^n )^n. |
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+0
3
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| 1, 1, 5, 28, 233, 2376, 28102, 379016, 5707025, 94439440, 1699067321, 32951077193, 684009742319, 15110032165151, 353485501643471, 8721374385748256, 226128389777924385, 6142306518887606112, 174311816444805024379
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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*k,n-k).
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EXAMPLE
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At n=4, a(4) = [x^4] (1 + x*(1+x)^4 )^4 = 233, since
(1 + x*(1+x)^4 )^4 = 1 + 4*x + 22*x^2 + 76*x^3 + 233*x^4 +...
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PROGRAM
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(PARI) a(n)=sum(k=0, n, binomial(n, k)*binomial(n*k, n-k))
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CROSSREFS
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Cf. variants: A121673, A121675-A121680.
Sequence in context: A107875 A038172 A000530 this_sequence A116977 A062796 A023887
Adjacent sequences: A121671 A121672 A121673 this_sequence A121675 A121676 A121677
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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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