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A199748
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a(n) = binomial(n*(3*n-1)/2, n).
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2
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1, 1, 10, 220, 7315, 324632, 18009460, 1198774720, 93080887185, 8258898672310, 824313388697656, 91408035226209520, 11149106984707682900, 1483408105790477598270, 213807915740948618992925, 33186033477308745271085760, 5518696446064784220490766525
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OFFSET
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0,3
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 0..300
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FORMULA
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a(n) = binomial(A000326(n), n), where A000326 are pentagonal numbers.
a(n) is divisible by 5 for gcd(n,5) = 1 and n>0.
a(n) ~ n^(n-1/2) * exp(n-2/3) * 3^n / (sqrt(Pi) * 2^(n+1/2)). - Vaclav Kotesovec, Apr 23 2015
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EXAMPLE
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a(2) = C(5,2) = 10; a(3) = C(12,3) = 220; a(4) = C(22,4) = 7315; a(5) = C(35,5) = 324632; ...
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MATHEMATICA
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Table[Binomial[n*(3n-1)/2, n], {n, 0, 20}] (* Harvey P. Dale, Aug 16 2012 *)
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PROG
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(PARI) {a(n)=binomial(n*(3*n-1)/2, n)}
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CROSSREFS
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Cf. A199747, A000326, A001318.
Sequence in context: A053131 A334908 A166181 * A210137 A064333 A223817
Adjacent sequences: A199745 A199746 A199747 * A199749 A199750 A199751
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna, Nov 09 2011
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STATUS
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approved
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