A303486 a(n) = n! * [x^n] 1/(1 - 3*x)^(n/3).

1, 1, 10, 162, 3640, 104720, 3674160, 152152000, 7264216960, 392841187200, 23734494784000, 1584471003315200, 115825295634048000, 9201578813819392000, 789383453851632640000, 72728093032166347776000, 7162140885524461957120000, 750766815289210771251200000

Offset: 0

Author

Ilya Gutkovskiy, Apr 24 2018

Keywords

• nonn

Examples

			a(1) = 1;
a(2) = 2*5 = 10;
a(3) = 3*6*9 = 162;
a(4) = 4*7*10*13 = 3640;
a(5) = 5*8*11*14*17 = 104720, etc.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..343
• Index entries for sequences related to factorial numbers

Crossrefs

Column k=3 of A303489.

Cf. A000407, A007559, A008544, A032031, A034000, A034001, A051604, A051605, A051606, A051607, A051608, A051609, A113551, A303487, A303488.

Programs

Mathematica

Table[n! SeriesCoefficient[1/(1 - 3 x)^(n/3), {x, 0, n}], {n, 0, 17}]
Table[Product[3 k + n, {k, 0, n - 1}], {n, 0, 17}]
Table[3^n Pochhammer[n/3, n], {n, 0, 17}]

Formula

a(n) = Product_{k=0..n-1} (3*k + n).

a(n) = 3^n*Gamma(4*n/3)/Gamma(n/3).

a(n) ~ 2^(8*n/3-1)*n^n/exp(n).