OFFSET
0,2
LINKS
Michael De Vlieger, Table of n, a(n) for n = 0..832
FORMULA
a(n) = (2*n)!*(2^(2*n)-1)/(2*n!*n!). [Corrected by Michel Marcus, Aug 22 2022]
From Peter Luschny, Aug 22 2022: (Start)
a(n) = (4^n - 1)*binomial(2*n, n) / 2.
a(n) = [x^n] ((1 - 16*x)^(-1/2) - (1 - 4*x)^(-1/2)) / 2. (End)
EXAMPLE
For n=2, we have these integers in base 2: 11, 101, 110, 1001, 1010, and 1100; so a(2) = 3+5+6+9+10+12 = 45.
MATHEMATICA
Array[(4^# - 1)*Binomial[2 #, #]/2 &, 20, 0] (* Michael De Vlieger, Aug 22 2022 *)
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Philippe LALLOUET (philip.lallouet(AT)wanadoo.fr), Aug 27 2007
EXTENSIONS
More terms from Peter Luschny, Aug 22 2022
STATUS
approved