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A052720
Expansion of e.g.f.: (1 - 4*x + 3*x^2)*(1 - 2*x - sqrt(1-4*x))/2 - x^2 + 2*x^3.
9
0, 0, 0, 0, 0, 0, 720, 30240, 1088640, 39916800, 1556755200, 65383718400, 2964061900800, 144815595724800, 7602818775552000, 427447366714368000, 25646842002862080000, 1636734826000834560000, 110752389892723138560000
OFFSET
0,7
LINKS
FORMULA
D-finite with recurrence: a(1)=0; a(2)=0; a(4)=0; a(3)=0; a(5)=0; a(6)=720; a(n+3) = (10+8*n)*a(n+2) + (22-27*n-19*n^2)*a(n+1) - (60-66*n+6*n^2+12*n^3)*a(n).
a(n) = n!*A003517(n-4). - R. J. Mathar, Oct 18 2013
From G. C. Greubel, May 28 2022: (Start)
G.f.: 6!*x^6*Hypergeometric2F0([3, 7/2], [], 4*x).
E.g.f.: (1/2)*(1 - 6*x + 9*x^2 - 2*x^3 - (1 - 4*x + 3*x^2)*sqrt(1-4*x)). (End)
MAPLE
spec := [S, {B=Union(Z, C), C=Prod(B, B), S=Prod(C, C, C)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
MATHEMATICA
Table[If[n<6, 0, 6*(n-2)!*Binomial[n-4, 2]*CatalanNumber[n-3]], {n, 0, 30}] (* G. C. Greubel, May 28 2022 *)
PROG
(SageMath)
def A052720(n):
if (n<6): return 0
else: return 6*factorial(n-2)*binomial(n-4, 2)*catalan_number(n-3)
[A052720(n) for n in (0..30)] # G. C. Greubel, May 28 2022
KEYWORD
easy,nonn
AUTHOR
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
STATUS
approved