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

0,2

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

Formula

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

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

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 *)

Prog

(PARI) x='x+O('x^30); Vec(serlaplace(1/(1-5*x)^(15/5))) \\ G. C. Greubel, Aug 15 2018
(Magma) m:=30; R<x>:=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

Crossrefs

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

Sequence in context: A375222 A009064 A049381 * A247238 A353145 A135390

Adjacent sequences: A051688 A051689 A051690 * A051692 A051693 A051694

Keyword

easy,nonn

Author

Wolfdieter Lang

Status

approved