OFFSET
0,3
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..100 (corrected by Ray Chandler, Jan 19 2019)
FORMULA
a(n) = Sum_{k=0..n/2} (2*k-1)!!^2 * binomial(n,2*k) * (1 + 2*k*(n-2*k)).
MATHEMATICA
a[n_] := Sum[(2*k-1)!!^2 * Binomial[n, 2*k] * (1 + 2*k*(n-2*k)), {k, 0, n/2} ]; Table[a[n], {n, 0, 21}] (* Jean-François Alcover, Nov 01 2017, after Andrew Howroyd *)
PROG
(PARI) a(n) = sum(k=0, n\2, ((2*k)!/(2^k*k!))^2 * binomial(n, 2*k) * (1 + 2*k*(n-2*k)));
CROSSREFS
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Oct 05 2017
STATUS
approved