A053105 a(n) = ((7*n+9)(!^7))/9(!^7), related to A034829 (((7*n+2)(!^7))/2 sept-, or 7-factorials).

1, 16, 368, 11040, 408480, 17973120, 916629120, 53164488960, 3455691782400, 248809808332800, 19655974858291200, 1690413837813043200, 157208486916613017600, 15720848691661301760000

Offset: 0

Author

Wolfdieter Lang

Keywords

• easy
• nonn

Comments

Row m=9 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)^(16/7))); [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, 15, 5!, 7}];lst (* Vladimir Joseph Stephan Orlovsky, Nov 08 2008 *)
CoefficientList[Series[1/(1-7x)^(16/7),{x,0,20}],x]Range[0,20]! (* Harvey P. Dale, Sep 11 2011 *)

PARI

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

Formula

a(n) = ((7*n+9)(!^7))/9(!^7)= A034829(n+2)/9.

E.g.f.: 1/(1-7*x)^(16/7).