A051691 a(n) = (5*n+10)(!^5)/10(!^5), related to A052562 ((5*n)(!^5) quintic, or 5-factorials).

1, 15, 300, 7500, 225000, 7875000, 315000000, 14175000000, 708750000000, 38981250000000, 2338875000000000, 152026875000000000, 10641881250000000000, 798141093750000000000, 63851287500000000000000

Offset: 0

Author

Wolfdieter Lang

Keywords

• easy
• nonn

Comments

Row m=10 of the array A(6; m,n) := ((5*n+m)(!^5))/m(!^5), m >= 0, n >= 0.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..352

Crossrefs

Cf. A052562, A008548(n+1), A034323(n+1), A034300(n+1), A034301(n+1), A034325(n+1), A051687-A051691 (rows m=0..10).

Programs

Magma

m:=30; R:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(1/(1-5*x)^(15/5))); [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, 14, 5!, 5}];lst (* Vladimir Joseph Stephan Orlovsky, Nov 08 2008 *)
With[{nn = 30}, CoefficientList[Series[1/(1 - 5*x)^(15/5), {x, 0, nn}], x]*Range[0, nn]!] (* G. C. Greubel, Aug 15 2018 *)

PARI

x='x+O('x^30); Vec(serlaplace(1/(1-5*x)^(15/5))) \\ G. C. Greubel, Aug 15 2018

Formula

a(n) = ((5*n+10)(!^5))/10(!^5) = A052562(n+2)/(5*10).

E.g.f.: 1/(1-5*x)^3.