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A303488 a(n) = n! * [x^n] 1/(1 - 5*x)^(n/5).

%I A303488 #5 Apr 24 2018 19:12:16
%S A303488 1,1,14,312,9576,375000,17873856,1004306688,65006637696,4763494479744,
%T A303488 389812500000000,35237024762075136,3487065897634615296,
%U A303488 374960171943074285568,43532820293400237735936,5427359437500000000000000,723181462895975365595529216,102563963819340862347122245632
%N A303488 a(n) = n! * [x^n] 1/(1 - 5*x)^(n/5).
%H A303488 <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>
%F A303488 a(n) = Product_{k=0..n-1} (5*k + n).
%F A303488 a(n) = 5^n*Gamma(6*n/5)/Gamma(n/5).
%F A303488 a(n) ~ 6^(6*n/5-1/2)*n^n/exp(n).
%e A303488 a(1) = 1;
%e A303488 a(2) = 2*7 = 14;
%e A303488 a(3) = 3*8*13 = 312;
%e A303488 a(4) = 4*9*14*19 = 9576;
%e A303488 a(5) = 5*10*15*20*25 = 375000, etc.
%t A303488 Table[n! SeriesCoefficient[1/(1 - 5 x)^(n/5), {x, 0, n}], {n, 0, 17}]
%t A303488 Table[Product[5 k + n, {k, 0, n - 1}], {n, 0, 17}]
%t A303488 Table[5^n Pochhammer[n/5, n], {n, 0, 17}]
%Y A303488 Column k=5 of A303489.
%Y A303488 Cf. A008546, A008548, A034300, A034301, A034323, A034325, A047055, A047056, A051687, A051688, A051689, A051690, A051691, A052562, A113551, A303486, A303487.
%K A303488 nonn
%O A303488 0,3
%A A303488 _Ilya Gutkovskiy_, Apr 24 2018