OFFSET
0,3
COMMENTS
Binomial transform of A097062.
LINKS
FORMULA
a(n) = (n-1)*2^(n-1) + 3*0^n/2.
a(n) = 4*a(n-1) - 4*a(n-2), n>2.
a(n) = Sum_{k=0..n} binomial(n, k)*((2k-1)/2 + 3*(-1)^k/2).
a(n+1)/2 = A001787(n).
From Amiram Eldar, Oct 01 2022: (Start)
Sum_{n>=2} 1/a(n) = log(2) (A002162).
Sum_{n>=2} (-1)^n/a(n) = log(3/2) (A016578). (End)
E.g.f.: (3 - exp(2*x)*(1 - 2*x))/2. - Stefano Spezia, Feb 12 2023
MATHEMATICA
CoefficientList[Series[(1-4x+6x^2)/(1-2x)^2, {x, 0, 30}], x] (* or *) Join[{1}, LinearRecurrence[{4, -4}, {0, 2}, 30]] (* Harvey P. Dale, May 26 2011 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Jul 22 2004
STATUS
approved