A053114 a(n) = ((8*n+9)(!^8))/9, related to A045755 ((8*n+1)(!^8) octo- or 8-factorials).

1, 17, 425, 14025, 575025, 28176225, 1606044825, 104392913625, 7620682694625, 617275298264625, 54937501545551625, 5328937649918507625, 559538453241443300625, 63227845216283092970625

Offset: 0

Author

Wolfdieter Lang

Keywords

• easy
• nonn

Comments

Row m=9 of the array A(9; m,n) := ((8*n+m)(!^8))/m(!^8), m >= 0, n >= 0.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..332

Crossrefs

Cf. A051189, A045755, A034908-12, A034975-6 (rows m=0..8).

Programs

Magma

m:=30; R:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(1/(1-8*x)^(17/8))); [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!, 8}];lst (* Vladimir Joseph Stephan Orlovsky, Nov 08 2008 *)
With[{nn = 30}, CoefficientList[Series[1/(1 - 8*x)^(17/8), {x, 0, nn}], x]*Range[0, nn]!] (* G. C. Greubel, Aug 16 2018 *)

PARI

x='x+O('x^30); Vec(serlaplace(1/(1-8*x)^(17/8))) \\ G. C. Greubel, Aug 16 2018

Formula

a(n) = ((8*n+9)(!^8))/9(!^8) = A045755(n+2)/9.

E.g.f.: 1/(1-8*x)^(17/8).

G.f.: 1/(1-17x/(1-8x/(1-25x/(1-16x/(1-33x/(1-24x/(1-41x/(1-32x/(1-... (continued fraction). - Philippe Deléham, Jan 07 2012