OFFSET
0,2
COMMENTS
Row m=8 of the array A(5; m,n) := ((4*n+m)(!^4))/m(!^4), m >= 0, n >= 0.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..363
FORMULA
a(n) = ((4*n+8)(!^4))/8(!^4) = A034177(n+2)/8.
E.g.f.: 1/(1-4*x)^3.
G.f.: G(0)/2, where G(k)= 1 + 1/(1 - 2*x/(2*x + 1/(2*k+6)/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, Jun 02 2013
MAPLE
G(x):=(1-4*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..15); # Zerinvary Lajos, Apr 04 2009
MATHEMATICA
s=1; lst={s}; Do[s+=n*s; AppendTo[lst, s], {n, 11, 5!, 4}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 08 2008 *)
With[{nn=20}, CoefficientList[Series[1/(1-4*x)^3, {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Mar 10 2017 *)
PROG
(PARI) x='x+O('x^30); Vec(serlaplace(1/(1-4*x)^(12/4))) \\ G. C. Greubel, Aug 15 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(1/(1-4*x)^(12/4))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Aug 15 2018
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
STATUS
approved