A051689 a(n) = (5*n+8)(!^5)/8(!^5), related to A034300 ((5*n+3)(!^5) quintic, or 5-factorials).

1, 13, 234, 5382, 150696, 4972968, 188972784, 8125829712, 390039826176, 20672110787328, 1198982425665024, 75535892816896512, 5136440711548962816, 374960171943074285568, 29246893411559794274304

Offset: 0

Author

Wolfdieter Lang

Keywords

• easy
• nonn

Comments

Row m=8 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)^(13/5))); [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, 12, 5!, 5}];lst (* Vladimir Joseph Stephan Orlovsky, Nov 08 2008 *)
With[{nn = 30}, CoefficientList[Series[1/(1 - 5*x)^(13/5), {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)^(13/5))) \\ G. C. Greubel, Aug 15 2018

Formula

a(n) = ((5*n+8)(!^5))/8(!^5) = A034300(n+2)/8.

E.g.f.: 1/(1-5*x)^(13/5).