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A138269
a(n+1) is the Hankel transform of C(n)+C(n+2), where C(n) = A000108(n).
0
1, 3, 12, 53, 231, 1000, 4329, 18747, 81188, 351597, 1522639, 6594000, 28556241, 123666803, 535556412, 2319302053, 10044062391, 43497219000, 188370799289, 815766130347, 3532789487188, 15299239691997
OFFSET
0,2
FORMULA
G.f.: (1-x)^2/(1-5*x+4*x^2-5*x^3+x^4).
a(n) = Re(P(2n,i)*CONJ(P(2n+1,i))) where i=sqrt(-1) and P(n,x) = Sum_{k=0..floor(n/2)} binomial(n-k,k) x^k.
a(n) = 5*a(n-1)-4*a(n-2)+5*a(n-3)-a(n-4). - Wesley Ivan Hurt, Mar 07 2022
MATHEMATICA
LinearRecurrence[{5, -4, 5, -1}, {1, 3, 12, 53}, 30] (* Harvey P. Dale, Dec 04 2022 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Mar 10 2008
STATUS
approved