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%I #20 Dec 23 2022 07:40:56
%S 1,10,130,2080,39520,869440,21736000,608608000,18866848000,
%T 641472832000,23734494784000,949379791360000,40823331028480000,
%U 1877873227310080000,92015788138193920000,4784820983186083840000,263165154075234611200000,15263578936363607449600000
%N a(n) = (3*n+7)!!!/7!!!.
%C Related to A007559(n+1) ((3*n+1)!!! triple factorials).
%C Row m=7 of the array A(4; m,n) := ((3*n+m)(!^3))/m(!^3), m >= 0, n >= 0.
%H G. C. Greubel, <a href="/A051607/b051607.txt">Table of n, a(n) for n = 0..378</a>
%F a(n) = ((3*n+7)(!^3))/7(!^3).
%F E.g.f.: 1/(1-3*x)^(10/3).
%F Sum_{n>=0} 1/a(n) = 1 + 9*(3*e)^(1/3)*(Gamma(10/3) - Gamma(10/3, 1/3)). - _Amiram Eldar_, Dec 23 2022
%t With[{nn = 30}, CoefficientList[Series[1/(1 - 3*x)^(10/3), {x, 0, nn}], x]*Range[0, nn]!] (* _G. C. Greubel_, Aug 15 2018 *)
%o (PARI) x='x+O('x^30); Vec(serlaplace(1/(1-3*x)^(10/3))) \\ _G. C. Greubel_, Aug 15 2018
%o (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(1/(1-3*x)^(10/3))); [Factorial(n-1)*b[n]: n in [1..m]]; // _G. C. Greubel_, Aug 15 2018
%Y Cf. A032031, A007559(n+1), A034000(n+1), A034001(n+1), A051604, A051605, A051606, A051608, A051609 (rows m=0..9).
%K easy,nonn
%O 0,2
%A _Wolfdieter Lang_