OFFSET
0,1
FORMULA
From Stefano Spezia, Aug 24 2023: (Start)
O.g.f.: (2*(sqrt(1 - 4*x) - 1) + x*(21 - 8*sqrt(1 - 4*x) - 50*x))/(x*(1 - 4*x)^(3/2)).
E.g.f.: exp(2*x)*((9 + 2*x)*BesselI(0, 2*x) + 2*(x - 2)*BesselI(1, 2*x)).
a(n) ~ c*4^n*sqrt(n), where c = A087197. (End)
MAPLE
[seq (binomial(2*n, n)*(n+3)^2/(n+1), n=0..25)];
MATHEMATICA
a[n_] := Binomial[2*n, n]*(n + 3)^2/(n + 1); Table[a[n], {n, 0, 25}] (* Robert P. P. McKone, Aug 25 2023 *)
PROG
(PARI) a(n) = binomial(2*n, n)/(n+1)*(n+3)^2 \\ Charles R Greathouse IV, Oct 23 2023
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Zerinvary Lajos, May 31 2006
EXTENSIONS
More terms from Stefano Spezia, Aug 24 2023
STATUS
approved