OFFSET
1,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (6,-13,12,-4).
FORMULA
Conjectures from Colin Barker, Mar 20 2012: (Start)
a(n) = -2^(-1+n)+(-1+2^n)*n.
G.f.: x^2*(4-7*x+2*x^2)/((1-x)^2*(1-2*x)^2). (End)
From Stefano Spezia, Nov 19 2023: (Start)
The above conjectures are true.
E.g.f.: exp(x)*(exp(x)*(4*x - 1) - 2*x)/2. (End)
MATHEMATICA
f[n_, k_] := n*Binomial[n, k] - Binomial[n - 1, k - 1]
Table[Sum[f[n, k], {k, 1, n}], {n, 1, 3 z}](* A208658 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Mar 01 2012
STATUS
approved