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!.

37837800, 2053230379200, 86825246363856000, 3434459445168687936000, 133396980694935715950192000, 5173935293233776678844146912000, 201687837026151453996918852912960000, 7920886423528046052820994110450678080000, 313629810506083768747620025974652020366480000

Offset

2,1

Comments

These are multinomial coefficients.

Links

Clark Kimberling, Table of n, a(n) for n = 2..200

Formula

a(n) ~ 3^(5/2) * 6^(6*n+1) / (Pi^(5/2)*n^(5/2)). - Vaclav Kotesovec, Oct 19 2014

Example

a(3) = 21!/(1!*2!*3!*4!*5!*6!) = 2053230379200.

Mathematica

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 *)

Prog

(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

Crossrefs

Cf. A000142, A001700, A248707, A248708, A248709.

Sequence in context: A206196 A272517 A246232 * A342350 A015365 A272599

Adjacent sequences: A248707 A248708 A248709 * A248711 A248712 A248713

Keyword

nonn,easy

Author

Clark Kimberling, Oct 12 2014

Status

approved