A053104 a(n) = ((7*n+8)(!^7))/8, related to A045754 ((7*n+1)(!^7) sept-, or 7-factorials).

1, 15, 330, 9570, 344520, 14814360, 740718000, 42220926000, 2702139264000, 191851887744000, 14964447244032000, 1271978015742720000, 117021977448330240000, 11585175767384693760000

Offset: 0

Author

Wolfdieter Lang

Keywords

• easy
• nonn

Comments

Row m=8 of the array A(8; m,n) := ((7*n+m)(!^7))/m(!^7), m >= 0, n >= 0.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..337

Crossrefs

Cf. A051188, A045754(n+1), A034829-34(n+1), A053104-A053106 (rows m=0..10).

Programs

Magma

m:=30; R:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(1/(1-7*x)^(15/7))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Aug 16 2018

Mathematica

s=1;lst={s};Do[s+=n*s;AppendTo[lst, s], {n, 14, 5!, 7}];lst (* Vladimir Joseph Stephan Orlovsky, Nov 08 2008 *)
With[{nn = 30}, CoefficientList[Series[1/(1 - 7*x)^(15/7), {x, 0, nn}], x]*Range[0, nn]!] (* G. C. Greubel, Aug 16 2018 *)

PARI

x='x+O('x^30); Vec(serlaplace(1/(1-7*x)^(15/7))) \\ G. C. Greubel, Aug 16 2018

Formula

a(n) = ((7*n+8)(!^7))/8(!^7) = A045754(n+2)/8.

E.g.f.: 1/(1-7*x)^(15/7).