A053116 a(n) = ((9*n+10)(!^9))/10, related to A045756 ((9*n+1)(!^9) 9-factorials).

1, 19, 532, 19684, 905464, 49800520, 3187233280, 232668029440, 19078778414080, 1736168835681280, 173616883568128000, 18924240308925952000, 2233060356453262336000, 283598665269564316672000, 38569418476660747067392000, 5592565679115808324771840000

Offset

0,2

Comments

Row m=10 of the array A(10; m,n) := ((9*n+m)(!^9))/m(!^9), m >= 0, n >= 0.

Links

G. C. Greubel, Table of n, a(n) for n = 0..327

Formula

a(n) = ((9*n+10)(!^9))/10(!^9) = A045756(n+2)/10.

E.g.f.: 1/(1-9*x)^(19/9).

Sum_{n>=0} 1/a(n) = 10 * (9*e)^(1/9) * (Gamma(10/9) - Gamma(10/9, 1/9)). - Amiram Eldar, Dec 15 2025

Mathematica

s=1; lst={s}; Do[s+=n*s; AppendTo[lst, s], {n, 18, 3*5!, 9}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 08 2008 *)
With[{nmax = 50}, CoefficientList[Series[1/(1 - 9*x)^(19/9), {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 - 9*x)^(19/9))) \\ G. C. Greubel, Aug 26 2018
(Magma) m:=25; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( 1/(1 - 9*x)^(19/9))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Aug 26 2018

Crossrefs

Row 19 of A392037.

Cf. A045756.

Sequence in context: A283382 A196512 A027406 * A309313 A158211 A278184

Adjacent sequences: A053113 A053114 A053115 * A053117 A053118 A053119

Keyword

easy,nonn

Author

Wolfdieter Lang

Status

approved