OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
FORMULA
From G. C. Greubel, Jun 17 2024: (Start)
a(n) = A000108(n-2)*(49*n^2 - 105*n + 48)/n - 6, for n >= 1, with a(0) = 1.
G.f.: (4 - 8*x + 5*x^2 - x^3 - (3 - x + 4*x^2)*sqrt(1-4*x))/((1-x)*sqrt(1-4*x)).
E.g.f.: (1/6)*( 18 + 24*x - 36*exp(x) + 4*exp(2*x)*(6 - 6*x + x^2) * BesselI(0, 2*x) + x*exp(2*x)*(23 - 4*x)*BesselI(1, 2*x) ). (End)
MATHEMATICA
Table[If[n==0, 1, CatalanNumber[n-2]*(49*n^2-105*n+48)/n -6], {n, 0, 40}] (* G. C. Greubel, Jun 17 2024 *)
PROG
(Magma) [n le 1 select n+1 else Catalan(n-2)*(49*n^2-105*n+48)/n - 6: n in [0..40]]; // G. C. Greubel, Jun 17 2024
(SageMath) [1, 2]+[catalan_number(n-2)*(49*n^2-105*n+48)/n -6 for n in range(2, 41)] # G. C. Greubel, Jun 17 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Sean A. Irvine, Oct 20 2019
STATUS
approved