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%I #18 Dec 23 2022 07:41:01
%S 1,11,154,2618,52360,1204280,31311280,908027120,29056867840,
%T 1016990374400,38645634227200,1584471003315200,69716724145868800,
%U 3276686034855833600,163834301742791680000,8683217992367959040000,486260207572605706240000,28689352246783736668160000
%N a(n) = (3*n+8)!!!/8!!!.
%C Related to A008544(n+1) ((3*n+2)!!! triple factorials).
%C Row m=8 of the array A(4; m,n) := ((3*n+m)(!^3))/m(!^3), m >= 0, n >= 0.
%H G. C. Greubel, <a href="/A051608/b051608.txt">Table of n, a(n) for n = 0..377</a>
%F a(n) = ((3*n+8)(!^3))/8(!^3).
%F E.g.f.: 1/(1-3*x)^(11/3).
%F Sum_{n>=0} 1/a(n) = 1 + 9*(9*e)^(1/3)*(Gamma(11/3) - Gamma(11/3, 1/3)). - _Amiram Eldar_, Dec 23 2022
%t With[{nn = 30}, CoefficientList[Series[1/(1 - 3*x)^(11/3), {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)^(11/3))) \\ _G. C. Greubel_, Aug 15 2018
%o (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(1/(1-3*x)^(11/3))); [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, A051607, A051609 (rows m=0..9).
%Y Cf. A008544.
%K easy,nonn
%O 0,2
%A _Wolfdieter Lang_
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