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A303487 a(n) = n! * [x^n] 1/(1 - 4*x)^(n/4).

%I A303487 #5 Apr 24 2018 19:12:09
%S A303487 1,1,12,231,6144,208845,8648640,422463195,23781703680,1515973484025,
%T A303487 107941254220800,8491022274509775,731304510986649600,
%U A303487 68444451854354701125,6916953288171902976000,750681472158682148959875,87076954662428278259712000,10751175443940144673035200625
%N A303487 a(n) = n! * [x^n] 1/(1 - 4*x)^(n/4).
%H A303487 <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>
%F A303487 a(n) = Product_{k=0..n-1} (4*k + n).
%F A303487 a(n) = 4^n*Gamma(5*n/4)/Gamma(n/4).
%F A303487 a(n) ~ 5^(5*n/4-1/2)*n^n/exp(n).
%e A303487 a(1) = 1;
%e A303487 a(2) = 2*6 = 12;
%e A303487 a(3) = 3*7*11 = 231;
%e A303487 a(4) = 4*8*12*16 = 6144;
%e A303487 a(5) = 5*9*13*17*21 = 208845, etc.
%t A303487 Table[n! SeriesCoefficient[1/(1 - 4 x)^(n/4), {x, 0, n}], {n, 0, 17}]
%t A303487 Table[Product[4 k + n, {k, 0, n - 1}], {n, 0, 17}]
%t A303487 Table[4^n Pochhammer[n/4, n], {n, 0, 17}]
%Y A303487 Column k=4 of A303489.
%Y A303487 Cf. A000407, A001813, A007696, A008545, A034176, A034177, A047053, A051617, A051618, A051619, A051620, A051621, A051622, A113551, A303486, A303488.
%K A303487 nonn
%O A303487 0,3
%A A303487 _Ilya Gutkovskiy_, Apr 24 2018