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A208658 Row sums of A208657. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
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
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Mar 01 2012
STATUS
approved

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Last modified May 25 01:50 EDT 2024. Contains 372782 sequences. (Running on oeis4.)