OFFSET
1,2
COMMENTS
a(n)/binomial(2*n-1,n-1) gives the mean distance of the n-odd graph.
Sum can be given in closed form involving four terms each consisting of a product of binomials and 3F2's.
LINKS
Eric Weisstein's World of Mathematics, Mean Distance
Eric Weisstein's World of Mathematics, Odd Graph
FORMULA
a(n) = 2*A136328(n)/binomial(2*n-1,n-1). - Andrew Howroyd, Mar 24 2018
MATHEMATICA
Table[Sum[k Binomial[n, Ceiling[k/2]] Binomial[n - 1, Floor[k/2]], {k, n - 1}], {n, 20}]
PROG
(PARI) T(n, k) = binomial(n, ceil(k/2))*binomial(n-1, k\2);
a(n) = sum(k=1, n-1, k*T(n, k)); \\ Altug Alkan, Mar 23 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Mar 23 2018
STATUS
approved