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A248710
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a(n) = f(6*n+3)/(f(n-2)*f(n-1)*f(n)*f(n+1)*f(n+2)*f(n+3)), where f(k) = k!.
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4
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37837800, 2053230379200, 86825246363856000, 3434459445168687936000, 133396980694935715950192000, 5173935293233776678844146912000, 201687837026151453996918852912960000, 7920886423528046052820994110450678080000, 313629810506083768747620025974652020366480000
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OFFSET
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2,1
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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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a(n) ~ 3^(5/2) * 6^(6*n+1) / (Pi^(5/2)*n^(5/2)). - Vaclav Kotesovec, Oct 19 2014
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EXAMPLE
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a(3) = 21!/(1!*2!*3!*4!*5!*6!) = 2053230379200.
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MATHEMATICA
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Table[(6 n + 3)!/((n - 2)! (n - 1)! n! (n + 1)! (n + 2)! (n + 3)!), {n, 2, 20}]
Table[(6n+3)!/Times@@((n+Range[-2, 3])!) , {n, 2, 20}] (* Harvey P. Dale, Jul 20 2020 *)
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PROG
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(Sage) [factorial(6*n + 3)/(factorial(n - 2)*factorial(n - 1)*factorial(n)*factorial(n + 1)*factorial(n + 2)*factorial(n + 3)) for n in range(2, 11)] # Stefano Spezia, Aug 16 2024
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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