A208658 Row sums of A208657.

0, 4, 17, 52, 139, 346, 825, 1912, 4343, 9718, 21493, 47092, 102387, 221170, 475121, 1015792, 2162671, 4587502, 9699309, 20447212, 42991595, 90177514, 188743657, 394264552, 822083559, 1711276006, 3556769765, 7381975012

Offset: 1

Author

Clark Kimberling, Mar 01 2012

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (6,-13,12,-4).

Crossrefs

Cf. A208657.

Programs

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 *)

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)