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

1, 9, 117, 1989, 41769, 1044225, 30282525, 999323325, 36974963025, 1515973484025, 68218806781125, 3342721532275125, 177164241210581625, 10098361749003152625, 616000066689192310125, 40040004334797500158125

Offset: 0

Author

Wolfdieter Lang

Keywords

• easy
• nonn

Comments

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

Links

• G. C. Greubel, Table of n, a(n) for n = 0..363

Crossrefs

Cf. A047053, A007696(n+1), A000407, A034176(n+1), A034177(n+1) (rows m=0..4).

Programs

Magma

m:=30; R:=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

Mathematica

s=1;lst={s};Do[s+=n*s;AppendTo[lst, s], {n, 8, 5!, 4}];lst (* Vladimir Joseph Stephan Orlovsky, Nov 08 2008 *)
With[{nn = 30}, CoefficientList[Series[1/(1 - 4*x)^(9/4), {x, 0, nn}], x]*Range[0, nn]!] (* G. C. Greubel, Aug 15 2018 *)

PARI

x='x+O('x^30); Vec(serlaplace(1/(1-4*x)^(9/4))) \\ G. C. Greubel, Aug 15 2018

Formula

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

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