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

1,2

Links

Table of n, a(n) for n=1..28.

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

Cf. A208657.

Sequence in context: A131339 A362173 A047668 * A092091 A046995 A001585

Adjacent sequences: A208655 A208656 A208657 * A208659 A208660 A208661

Keyword

nonn,easy

Author

Clark Kimberling, Mar 01 2012

Status

approved