A053115 a(n) = ((8*n+10)(!^8))/20, related to A034908 ((8*n+2)(!^8) octo- or 8-factorials).

1, 18, 468, 15912, 668304, 33415200, 1938081600, 127913385600, 9465590534400, 776178423820800, 69856058143872000, 6845893698099456000, 725664731998542336000, 82725779447833826304000, 10092545092635726809088000, 1312030862042644485181440000, 181060258961884938955038720000

Offset

0,2

Comments

Row m=10 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

Formula

a(n) = ((8*n+10)(!^8))/10(!^8) = A034908(n+2)/10.

E.g.f.: 1/(1-8*x)^(9/4).

G.f.: 1/(1-18x/(1-8x/(1-26x/(1-16x/(1-34x/(1-24x/(1-42x/(1-32x/(1-... (continued fraction). - Philippe Deléham, Jan 07 2012

Sum_{n>=0} 1/a(n) = 10 * 2^(3/4) * exp(1/8) * (Gamma(5/4) - Gamma(5/4, 1/8)). - Amiram Eldar, Dec 15 2025

Mathematica

s=1; lst={s}; Do[s+=n*s; AppendTo[lst, s], {n, 17, 5!, 8}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 08 2008 *)
With[{nmax = 50}, CoefficientList[Series[1/(1 - 8*x)^(9/4), {x, 0, nmax}], x]*Range[0, nmax]!] (* G. C. Greubel, Aug 26 2018 *)

Prog

(PARI) my(x='x+O('x^25)); Vec(serlaplace(1/(1-8*x)^(9/4))) \\ G. C. Greubel, Aug 26 2018
(Magma) m:=25; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(1/(1-8*x)^(9/4))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Aug 26 2018

Crossrefs

Cf. A051189, A045755, A034908-12, A034975-6, A053114 (rows m=0..9).

Sequence in context: A086501 A204241 A386830 * A084273 A386771 A230587

Adjacent sequences: A053112 A053113 A053114 * A053116 A053117 A053118

Keyword

easy,nonn

Author

Wolfdieter Lang

Status

approved