A052392 T(2n+1,n), array T as in A054120.
1, 6, 39, 261, 1779, 12288, 85734, 602871, 4265859, 30338604, 216677490, 1552999242, 11164548078, 80471658192, 581340627372, 4208086875915, 30514467991011, 221620953353844, 1611867544369146, 11738194502675910, 85580528620970874, 624605115244327776, 4563036506245946964
Offset: 0
Keywords
Links
- Robert Israel, Table of n, a(n) for n = 0..1145
Programs
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Maple
T:= proc(n,k) option remember; if k=0 or k=n then return 1 fi; if k > n then return 0 fi; procname(n-1,k-1) + 2*procname(n-2,k-1) + procname(n-1,k) end proc; T(2,1):= 3: seq(T(2*n+1,n),n=0..30); # Robert Israel, Nov 26 2018
Formula
From Robert Israel, Nov 26 2018: (Start)
Empirical g.f.: (2*x^2-3*x+1)/(2*sqrt(4*x^2-8*x+1)*x)+(x-1)/(2*x).
Empirical recurrence: 8*n*a(n)+(-32-28*n)*a(1+n)+(78+30*n)*a(n+2)+(-45-11*n)*a(n+3)+(5+n)*a(n+4)=0. (End)