A384302 a(n) = Product_{k=0..2*n-1} (3*n+k).
1, 12, 3024, 2162160, 3047466240, 7117005772800, 24858235898496000, 121350057687226368000, 789024790105300869120000, 6591440263482135279009792000, 68796453067268024353471856640000, 877296253184539514911686618316800000, 13421187715188797689536009541110988800000
Offset: 0
Programs
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PARI
a(n) = (2*n)!*binomial(5*n-1, 2*n);
Formula
a(n) = RisingFactorial(3*n,2*n).
a(n) = (2*n)! * [x^(2*n)] 1/(1 - x)^(3*n).
a(n) = (2*n)! * binomial(5*n-1,2*n).
D-finite with recurrence 3*(3*n-1)*(3*n-2)*a(n) -5*(5*n-4)*(5*n-3)*(5*n-2)*(5*n-1)*a(n-1)=0. - R. J. Mathar, May 26 2025