A053106 a(n) = ((7*n+10)(!^7))/10(1^7), related to A034830 (((7*n+3)(!^7))/3 sept-, or 7-factorials).

1, 17, 408, 12648, 480624, 21628080, 1124660160, 66354949440, 4379426663040, 319698146401920, 25575851712153600, 2225099098957363200, 209159315301992140800, 21125090845501206220800

Offset: 0

Author

Wolfdieter Lang

Keywords

• easy
• nonn

Comments

Row m=10 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-A034834(n+1), A053104-A053106 (rows m=0..10).

Programs

Magma

m:=30; R:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(1/(1-7*x)^(17/7))); [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, 16, 5!, 7}];lst (* Vladimir Joseph Stephan Orlovsky, Nov 08 2008 *)
With[{nn = 30}, CoefficientList[Series[1/(1 - 7*x)^(17/7), {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)^(17/7))) \\ G. C. Greubel, Aug 16 2018

Formula

a(n) = ((7*n+10)(!^7))/10(!^7) = A034830(n+2)/10.

E.g.f.: 1/(1-7*x)^(17/7).