OFFSET
0,2
COMMENTS
Row m=6 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..378
FORMULA
a(n) = ((3*n+6)(!^3))/6(!^3); e.g.f.: 1/(1-3*x)^3.
a(n) = n!*3^(n-2)/2, n >= 2. - Zerinvary Lajos, Sep 23 2006
Sum_{n>=0} 1/a(n) = 18*exp(1/3) - 24. - Amiram Eldar, Dec 18 2022
MAPLE
[seq(n!*3^(n-2)/2, n=2..18)]; # Zerinvary Lajos, Sep 23 2006
with(combstruct):ZL:=[T, {T=Union(Z, Prod(Epsilon, Z, T), Prod(T, Z, Epsilon), Prod(T, Z))}, labeled]:seq(count(ZL, size=i)/6, i=2..18); # Zerinvary Lajos, Dec 16 2007
restart: G(x):=(1-3*x)^(n-4): 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..16); # Zerinvary Lajos, Apr 04 2009
MATHEMATICA
With[{nn = 30}, CoefficientList[Series[1/(1 - 3*x)^(9/3), {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)^(9/3))) \\ G. C. Greubel, Aug 15 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(1/(1-3*x)^(9/3))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Aug 15 2018
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
STATUS
approved