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%I #14 Sep 08 2022 08:44:59
%S 1,11,165,3135,72105,1946835,60351885,2112315975,82380323025,
%T 3542353890075,166490632833525,8491022274509775,467006225098037625,
%U 27553367280784219875,1735862138689405852125,116302763292190192092375
%N a(n) = (4*n+7)(!^4)/7(!^4), related to A034176(n+1) ((4*n+3)(!^4) quartic, or 4-factorials).
%C Row m=7 of the array A(5; m,n) := ((4*n+m)(!^4))/m(!^4), m >= 0, n >= 0.
%H G. C. Greubel, <a href="/A051619/b051619.txt">Table of n, a(n) for n = 0..363</a>
%F a(n) = ((4*n+7)(!^4))/7(!^4) = A034176(n+2)/7.
%F E.g.f.: 1/(1-4*x)^(11/4).
%t s=1;lst={s};Do[s+=n*s;AppendTo[lst, s], {n, 10, 5!, 4}];lst (* _Vladimir Joseph Stephan Orlovsky_, Nov 08 2008 *)
%t With[{nn = 30}, CoefficientList[Series[1/(1 - 4*x)^(11/4), {x, 0, nn}], x]*Range[0, nn]!] (* _G. C. Greubel_, Aug 15 2018 *)
%o (PARI) x='x+O('x^30); Vec(serlaplace(1/(1-4*x)^(11/4))) \\ _G. C. Greubel_, Aug 15 2018
%o (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(1/(1-4*x)^(11/4))); [Factorial(n-1)*b[n]: n in [1..m]]; // _G. C. Greubel_, Aug 15 2018
%Y Cf. A047053, A007696(n+1), A000407, A034176(n+1), A034177(n+1), A051617-A051622 (rows m=0..10).
%K easy,nonn
%O 0,2
%A _Wolfdieter Lang_
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