OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
FORMULA
G.f.: (6*x-1)/sqrt(1-4*x)^3 - 1/(x-1).
a(n) ~ sqrt(n)*4^n/sqrt(Pi). - Vaclav Kotesovec, Feb 14 2014
From Gregory Morse, Mar 19 2021: (Start)
a(n) = (2*n)!*(n-1)/(n!)^2 + 1.
a(n) = A030662(n-1)*(n-1) + n, for n > 0. (End)
E.g.f.: exp(x) * (1 - exp(x) * ((1 - 2*x) * BesselI(0,2*x) - 2 * x * BesselI(1,2*x))). - Ilya Gutkovskiy, Nov 19 2021
MAPLE
a:= proc(n) option remember; `if`(n<2, n,
((n-1)*(3*n-4)*(5*n-3) *a(n-1)
-2*(2*n-3)*(3*n^2-4*n+2) *a(n-2))/
(n*(3*n^2-10*n+9)))
end:
seq(a(n), n=0..30);
MATHEMATICA
CoefficientList[Series[(6*x-1)/Sqrt[1-4*x]^3-1/(x-1), {x, 0, 20}], x] (* Vaclav Kotesovec, Feb 14 2014 *)
a[n_] := Module[{m}, InterpolatingPolynomial[Table[{k, If[k == n, n, 1]}, {k, 0, n}], m] /. m -> 2n];
a /@ Range[0, 30] (* Jean-François Alcover, Dec 22 2020 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Feb 11 2014
STATUS
approved