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

%I A303486 #8 Aug 16 2018 06:02:26
%S A303486 1,1,10,162,3640,104720,3674160,152152000,7264216960,392841187200,
%T A303486 23734494784000,1584471003315200,115825295634048000,
%U A303486 9201578813819392000,789383453851632640000,72728093032166347776000,7162140885524461957120000,750766815289210771251200000
%N A303486 a(n) = n! * [x^n] 1/(1 - 3*x)^(n/3).
%H A303486 G. C. Greubel, <a href="/A303486/b303486.txt">Table of n, a(n) for n = 0..343</a>
%H A303486 <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>
%F A303486 a(n) = Product_{k=0..n-1} (3*k + n).
%F A303486 a(n) = 3^n*Gamma(4*n/3)/Gamma(n/3).
%F A303486 a(n) ~ 2^(8*n/3-1)*n^n/exp(n).
%e A303486 a(1) = 1;
%e A303486 a(2) = 2*5 = 10;
%e A303486 a(3) = 3*6*9 = 162;
%e A303486 a(4) = 4*7*10*13 = 3640;
%e A303486 a(5) = 5*8*11*14*17 = 104720, etc.
%t A303486 Table[n! SeriesCoefficient[1/(1 - 3 x)^(n/3), {x, 0, n}], {n, 0, 17}]
%t A303486 Table[Product[3 k + n, {k, 0, n - 1}], {n, 0, 17}]
%t A303486 Table[3^n Pochhammer[n/3, n], {n, 0, 17}]
%Y A303486 Column k=3 of A303489.
%Y A303486 Cf. A000407, A007559, A008544, A032031, A034000, A034001, A051604, A051605, A051606, A051607, A051608, A051609, A113551, A303487, A303488.
%K A303486 nonn
%O A303486 0,3
%A A303486 _Ilya Gutkovskiy_, Apr 24 2018