A248707
a(n) = f(3*n)/(f(n-1)*f(n)*f(n+1)), where f(k) = k!.
Original entry on oeis.org
3, 60, 1260, 27720, 630630, 14702688, 349188840, 8413788240, 205086088350, 5046360719400, 125149745841120, 3124367780788800, 78443948210518800, 1979201154850012800, 50151543548788717200, 1275619260617425959840, 32554866547007225016750, 833323952354971320243000
Offset: 1
a(2) = 6!/(1!*2!*3!) = 60.
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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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Table[(3 n)!/((n - 1)! n! (n + 1)!), {n, 1, 20}]
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a(n) = (3*n)! / ((n-1)!*n!*(n+1)!); \\ Amiram Eldar, Jun 11 2025
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[3*factorial(3*n-1)/(factorial(n-1)^3*n*(n+1)) for n in range(1,19)] # Stefano Spezia, Aug 16 2024
A248708
a(n) = f(4*n+2)/(f(n-1)*f(n)*f(n+1)*f(n+2)), where f(k) = k!.
Original entry on oeis.org
60, 12600, 2522520, 514594080, 107550162720, 22969641895200, 4995897112206000, 1103284402265073600, 246784661070292144800, 55803246694136969227200, 12736017918577260592084800, 2930174751896446667689440000, 678879630375093886522676256000, 158257286142440155623613107216000
Offset: 1
a(2) = 10!/(1!*2!*3!*4!) = 12600.
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Table[(4 n + 2)!/((n - 1)! n! (n + 1)! (n + 2)!), {n, 1, 20}]
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[factorial(4*n + 2)/(factorial(n - 1)* factorial(n)*factorial(n + 1)*factorial(n + 2)) for n in range(1,14)] # Stefano Spezia, Aug 16 2024
A248710
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!.
Original entry on oeis.org
37837800, 2053230379200, 86825246363856000, 3434459445168687936000, 133396980694935715950192000, 5173935293233776678844146912000, 201687837026151453996918852912960000, 7920886423528046052820994110450678080000, 313629810506083768747620025974652020366480000
Offset: 2
a(3) = 21!/(1!*2!*3!*4!*5!*6!) = 2053230379200.
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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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[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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