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A248707
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a(n) = f(3*n)/(f(n-1)*f(n)*f(n+1)), where f(k) = k!.
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4
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3, 60, 1260, 27720, 630630, 14702688, 349188840, 8413788240, 205086088350, 5046360719400, 125149745841120, 3124367780788800, 78443948210518800, 1979201154850012800, 50151543548788717200, 1275619260617425959840, 32554866547007225016750, 833323952354971320243000
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OFFSET
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1,1
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COMMENTS
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These are multinomial coefficients.
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LINKS
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FORMULA
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G.f.: 3*x*hypergeom([4/3, 5/3], [3], 27*x).
n*(n+2)*a(n+1) = 3*(3*n+1)(3*n+2)*a(n). (End)
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EXAMPLE
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a(2) = 6!/(1!*2!*3!) = 60.
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MAPLE
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seq(3*(3*n-1)!/((n-1)!^3*n*(n+1)), n=1..20); # Robert Israel, Mar 02 2017
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MATHEMATICA
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Table[(3 n)!/((n - 1)! n! (n + 1)!), {n, 1, 20}]
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PROG
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(Sage) [3*factorial(3*n-1)/(factorial(n-1)^3*n*(n+1)) for n in range(1, 19)] # Stefano Spezia, Aug 16 2024
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CROSSREFS
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KEYWORD
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nonn,easy,changed
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AUTHOR
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STATUS
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approved
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