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A051621 a(n) = (4*n+9)(!^4)/9(!^4), related to A007696(n+1) ((4*n+1)(!^4) quartic, or 4-factorials). 4

%I

%S 1,13,221,4641,116025,3364725,111035925,4108329225,168441498225,

%T 7579867420125,371413503586125,19684915690064625,1122040194333683625,

%U 68444451854354701125,4448889370533055573125,306973366566780834545625

%N a(n) = (4*n+9)(!^4)/9(!^4), related to A007696(n+1) ((4*n+1)(!^4) quartic, or 4-factorials).

%C Row m=9 of the array A(5; m,n) := ((4*n+m)(!^4))/m(!^4), m >= 0, n >= 0.

%H G. C. Greubel, <a href="/A051621/b051621.txt">Table of n, a(n) for n = 0..363</a>

%F a(n) = ((4*n+9)(!^4))/9(!^4) = A007696(n+3)/(5*9).

%F E.g.f.: 1/(1-4*x)^(13/4).

%t s=1;lst={s};Do[s+=n*s;AppendTo[lst, s], {n, 12, 5!, 4}];lst (* _Vladimir Joseph Stephan Orlovsky_, Nov 08 2008 *)

%t With[{nn = 30}, CoefficientList[Series[1/(1 - 4*x)^(13/4), {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)^(13/4))) \\ _G. C. Greubel_, Aug 15 2018

%o (MAGMA) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(1/(1-4*x)^(13/4))); [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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Last modified October 16 20:35 EDT 2019. Contains 328103 sequences. (Running on oeis4.)