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A026619
a(n) = A026615(2*n-1, n-1).
16
1, 5, 17, 60, 217, 798, 2970, 11154, 42185, 160446, 613054, 2351440, 9048522, 34916300, 135059220, 523521630, 2033066025, 7908332190, 30807696150, 120173896920, 469334610030, 1834970026500
OFFSET
1,2
LINKS
FORMULA
From G. C. Greubel, Jun 13 2024: (Start)
a(n) = (7*n - 4)*binomial(2*n, n)/(4*(2*n-1)) -(1/2)*[n=1].
G.f.: ( (2 - x) - (2 + x)*sqrt(1-4*x) )/(2*sqrt(1-4*x))
E.g.f.: (1/2)*exp(2*x)*( (2 - x)*BesselI(0, 2*x) + x*BesselI(1, 2*x) ) - (1 + x/2). (End)
MATHEMATICA
Table[(7*n-4)*Binomial[2*n, n]/(4*(2*n-1)) -(1/2)*Boole[n==1], {n, 40}] (* G. C. Greubel, Jun 13 2024 *)
PROG
(Magma) [n eq 1 select 1 else (7*n-4)*(n+1)*Catalan(n)/(4*(2*n-1)): n in [1..40]]; // G. C. Greubel, Jun 13 2024
(SageMath) [(7*n-4)*binomial(2*n, n)/(4*(2*n-1)) -(1/2)*int(n==1) for n in range(1, 41)] # G. C. Greubel, Jun 13 2024
KEYWORD
nonn
STATUS
approved