A051688 a(n) = (5*n+7)(!^5)/7(!^5), related to A034323 ((5*n+2)(!^5) quintic, or 5-factorials).

1, 12, 204, 4488, 121176, 3877632, 143472384, 6025840128, 283214486016, 14727153272832, 839447736551424, 52045759666188288, 3487065897634615296, 251068744629692301312, 19332293336486307201024

Offset: 0

Author

Wolfdieter Lang

Keywords

• easy
• nonn

Comments

Row m=7 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..353

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)^(12/5))); [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, 11, 5!, 5}];lst (* Vladimir Joseph Stephan Orlovsky, Nov 08 2008 *)
With[{nn = 30}, CoefficientList[Series[1/(1 - 5*x)^(12/5), {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)^(12/5))) \\ G. C. Greubel, Aug 15 2018

Formula

a(n) = ((5*n+7)(!^5))/7(!^5) = A034323(n+2)/7.

E.g.f.: 1/(1-5*x)^(12/5).