|
|
A052715
|
|
Expansion of e.g.f. (1-2*x-sqrt(1-4*x))/2 - x*(1-2*x-sqrt(1-4*x)) - x^2.
|
|
10
|
|
|
0, 0, 0, 0, 24, 480, 10080, 241920, 6652800, 207567360, 7264857600, 282291609600, 12067966310400, 563171761152000, 28496491114291200, 1554354060779520000, 90929712555601920000, 5679609738088366080000
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,5
|
|
LINKS
|
|
|
FORMULA
|
D-finite with recurrence: a(1)=0; a(2)=0; a(3)=0; a(4)=24; 4*(-n-3+2*n^2)*a(n) +2*(-1-3*n)*a(n+1) +a(n+2) =0.
|
|
MAPLE
|
spec := [S, {B=Union(Z, C), C=Prod(B, B), S=Prod(C, C)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
|
|
MATHEMATICA
|
With[{nn=20}, CoefficientList[Series[(1-2x-Sqrt[1-4x])/2-x(1-2x- Sqrt[ 1-4x])- x^2, {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Jul 18 2016 *)
|
|
PROG
|
(Magma) [n le 3 select 0 else 2*(n-3)*Factorial(n-1)*Catalan(n-2): n in [0..30]]; // G. C. Greubel, May 27 2022
(SageMath) [0]+[4*factorial(n-1)*binomial(2*n-5, n-4) for n in (1..30)] # G. C. Greubel, May 27 2022
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
|
|
STATUS
|
approved
|
|
|
|