|
|
A052676
|
|
Expansion of e.g.f. 3*x/(1 - 2*x).
|
|
1
|
|
|
0, 3, 12, 72, 576, 5760, 69120, 967680, 15482880, 278691840, 5573836800, 122624409600, 2942985830400, 76517631590400, 2142493684531200, 64274810535936000, 2056793937149952000, 69930993863098368000, 2517515779071541248000, 95665599604718567424000
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
FORMULA
|
E.g.f.: 3*x/(1 - 2*x).
Recurrence: a(0) = 0, a(1) = 3, a(n) = 2*n*a(n-1).
a(n) = 3*2^(n-1)*n! for n > 0.
G.f.: (3/2)*(Hypergeometric2F0([1, 1], [], 2*x) - 1). - G. C. Greubel, Jun 12 2022
|
|
MAPLE
|
spec := [S, {S=Prod(Sequence(Union(Z, Z)), Union(Z, Z, Z))}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
|
|
MATHEMATICA
|
With[{nn=20}, CoefficientList[Series[(3x)/(1-2x), {x, 0, nn}], x]Range[0, nn]!] (* Harvey P. Dale, Feb 23 2013 *)
|
|
PROG
|
(Magma) [0] cat [3*Factorial(n)*2^(n-1): n in [1..30]]; // G. C. Greubel, Jun 12 2022
(SageMath) [(3/2)*(factorial(n)*2^n -bool(n==0)) for n in (0..30)] # G. C. Greubel, Jun 12 2022
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
|
|
STATUS
|
approved
|
|
|
|