A384300 a(n) = Product_{k=0..2*n-1} (3*n+k-2).
1, 2, 840, 665280, 980179200, 2346549004800, 8326896754176000, 41098950018846720000, 269397128065642536960000, 2264501147602213494374400000, 23751156416080627455365283840000, 304080322557324667642345606348800000, 4667216066941750219330172809445376000000
Offset: 0
Programs
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PARI
a(n) = (2*n)!*binomial(5*n-3, 2*n);
Formula
a(n) = RisingFactorial(3*n-2,2*n).
a(n) = (2*n)! * [x^(2*n)] 1/(1 - x)^(3*n-2).
a(n) = (2*n)! * binomial(5*n-3,2*n).
D-finite with recurrence 3*(3*n-4)*(3*n-5)*a(n) -5*(5*n-4)*(5*n-3)*(5*n-7)*(5*n-6)*a(n-1)=0. - R. J. Mathar, May 26 2025