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A051617 a(n) = (4*n+5)(!^4)/5(!^4), related to A007696(n+1) ((4*n+1)(!^4) quartic, or 4-factorials). 8

%I

%S 1,9,117,1989,41769,1044225,30282525,999323325,36974963025,

%T 1515973484025,68218806781125,3342721532275125,177164241210581625,

%U 10098361749003152625,616000066689192310125,40040004334797500158125

%N a(n) = (4*n+5)(!^4)/5(!^4), related to A007696(n+1) ((4*n+1)(!^4) quartic, or 4-factorials).

%C Row m=5 of the array A(5; m,n) := ((4*n+m)(!^4))/m(!^4), m >= 0, n >= 0.

%H G. C. Greubel, <a href="/A051617/b051617.txt">Table of n, a(n) for n = 0..363</a>

%F a(n) = ((4*n+5)(!^4))/5(!^4).

%F E.g.f.: 1/(1-4*x)^(9/4).

%t s=1;lst={s};Do[s+=n*s;AppendTo[lst, s], {n, 8, 5!, 4}];lst (* _Vladimir Joseph Stephan Orlovsky_, Nov 08 2008 *)

%t With[{nn = 30}, CoefficientList[Series[1/(1 - 4*x)^(9/4), {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)^(9/4))) \\ _G. C. Greubel_, Aug 15 2018

%o (MAGMA) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(1/(1-4*x)^(9/4))); [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) (rows m=0..4).

%K easy,nonn

%O 0,2

%A _Wolfdieter Lang_

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Last modified October 17 08:36 EDT 2019. Contains 328107 sequences. (Running on oeis4.)