OFFSET
0,2
COMMENTS
Row m=9 of the array A(4; m,n) := ((3*n+m)(!^3))/m(!^3), m >= 0, n >= 0.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..377
FORMULA
a(n) = ((3*n+9)(!^3))/9(!^3).
E.g.f.: 1/(1-3*x)^4.
From Amiram Eldar, Dec 18 2022: (Start)
a(n) = (n+3)!*3^(n-1)/2.
Sum_{n>=0} 1/a(n) = 162*exp(1/3) - 225. (End)
MAPLE
restart: G(x):=(1-3*x)^(n-5): f[0]:=G(x): for n from 1 to 29 do f[n]:=diff(f[n-1], x) od:x:=0:seq(f[n], n=0..15); # Zerinvary Lajos, Apr 04 2009
MATHEMATICA
With[{nn = 30}, CoefficientList[Series[1/(1 - 3*x)^(12/3), {x, 0, nn}], x]*Range[0, nn]!] (* G. C. Greubel, Aug 15 2018 *)
PROG
(PARI) x='x+O('x^30); Vec(serlaplace(1/(1-3*x)^(12/3))) \\ G. C. Greubel, Aug 15 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(1/(1-3*x)^(12/3))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Aug 15 2018
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
STATUS
approved