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

Offset: 0

Author

Wolfdieter Lang

Keywords

• easy
• nonn

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

Crossrefs

Cf. A051232, A045756, A035012-3, A035017-8, A035020-3 (rows m=0..9).

Programs

Magma

m:=25; R:=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

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 *)

PARI

x='x+O('x^25); Vec(serlaplace(1/(1 - 9*x)^(19/9))) \\ G. C. Greubel, Aug 26 2018

Formula

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

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