OFFSET
0,2
COMMENTS
Hankel transform is A141354.
FORMULA
G.f.: c(x)+2x/(1-2x), where c(x) is the g.f. of A000108. [corrected by Paul Barry, Oct 18 2010]
Conjecture: (n+1)*a(n) + 2*(-4*n+1)*a(n-1) + 4*(5*n-7)*a(n-2) + 8*(-2*n+5)*a(n-3) = 0. - R. J. Mathar, Nov 15 2012
MATHEMATICA
f[n_] := Binomial[2n, n]/(n + 1) + 2^n - 0^n; f[0] = 1; Array[f, 29, 0] (* or *)
CoefficientList[ Series[1 + 1/2 (-4 + 2/(1 - 2x) + (1 - Sqrt[1 - 4x])/x), {x, 0, 28}], x] (* Robert G. Wilson v, Mar 18 2018 *)
PROG
(PARI) a(n) = binomial(2*n, n)/(n+1) + 2^n - 0^n; \\ Michel Marcus, Mar 18 2018
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Jun 27 2008
STATUS
approved