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Search: id:A121678
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| A121678 |
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a(n) = [x^n] (1 + x*(1+x)^n )^(n+1). |
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+0
4
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| 1, 2, 9, 52, 425, 4236, 49294, 655096, 9731313, 159114880, 2832245911, 54400757016, 1119436524947, 24532373640334, 569732648555295, 13962373137304496, 359767723241891425, 9715902692094061488
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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) = A121679(n).
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FORMULA
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a(n) = Sum_{k=0..n+1} C(n+1,k) * C(n*k,n-k).
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EXAMPLE
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At n=5, a(5) = [x^5] (1 + x*(1+x)^5)^6 = 4236, since
(1+x*(1+x)^5)^6 = 1 + 6*x + 45*x^2 + 230*x^3 + 1050*x^4 + 4236*x^5 +...
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PROGRAM
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(PARI) a(n)=sum(k=0, n+1, binomial(n+1, k)*binomial(n*k, n-k))
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CROSSREFS
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Cf. A121679; variants: A121673-A121676, A121680.
Sequence in context: A143922 A110322 A161631 this_sequence A124347 A080146 A074602
Adjacent sequences: A121675 A121676 A121677 this_sequence A121679 A121680 A121681
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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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