A185251 a(n) = Sum_{k=0..floor(n/2)} k*binomial(n,k).
0, 0, 2, 3, 16, 25, 96, 154, 512, 837, 2560, 4246, 12288, 20618, 57344, 97140, 262144, 447661, 1179648, 2028478, 5242880, 9070110, 23068672, 40122028, 100663296, 175913250, 436207616, 765561564, 1879048192, 3310623412, 8053063680, 14238676712, 34359738368
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
Programs
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Maple
seq(n*2^(n-2) - `if`(type(n,even), 0, binomial(n-1, (n-1)/2)*n/2) ,n=0..32); # Mark van Hoeij, May 12 2013
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Mathematica
Table[Sum[k Binomial[n, k], {k, 0, Floor[n/2]}], {n, 0, 40}] (* Harvey P. Dale, Nov 25 2012 *) -
PARI
a(n)=sum(k=0,n\2,k*binomial(n,k))