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A052711
Expansion of e.g.f. x*(1 - 2*x - sqrt(1-4*x))/2.
9
0, 0, 0, 6, 48, 600, 10080, 211680, 5322240, 155675520, 5189184000, 194075481600, 8045310873600, 366061644748800, 18134130709094400, 971471287987200000, 55956746188062720000, 3448334483839365120000
OFFSET
0,4
LINKS
FORMULA
D-finite with recurrence: a(1)=0, a(2)=0, a(3)=6, a(4)=48, n*a(n+1) = 2*(n+1)*(2*n-3)*a(n).
From R. J. Mathar, Oct 18 2013: (Start)
a(n) = n!*A000108(n-2).
a(n) = A052717(n), n>2. (End)
G.f.: x*(1 - 4*x - 2F0([-1/2,2], [], 4*x))/2. - R. J. Mathar, Jan 25 2020
MAPLE
spec := [S, {C=Union(B, Z), B=Prod(C, C), S=Prod(B, Z)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
MATHEMATICA
With[{nn=20}, CoefficientList[Series[x (1-2x-Sqrt[1-4x])/2, {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Mar 05 2016 *)
Table[n!*CatalanNumber[n-2] +Boole[n==1] -2*Boole[n==2], {n, 0, 30}] (* G. C. Greubel, May 30 2022 *)
PROG
(SageMath) [factorial(n)*catalan_number(n-2) + bool(n==1)/2 - 2*bool(n==2) for n in (0..30)] # G. C. Greubel, May 30 2022
KEYWORD
easy,nonn
AUTHOR
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
STATUS
approved