OFFSET
0,2
COMMENTS
a(n) = sum{k=0..n} sum{i=k..n} binomial(n-k,n-i)*(2i+1)$
where i$ denotes the swinging factorial of i (A056040).
LINKS
Peter Luschny, Swinging Factorial.
MAPLE
swing := proc(n) option remember; if n = 0 then 1 elif
irem(n, 2) = 1 then swing(n-1)*n else 4*swing(n-1)/n fi end:
a := proc(n) local i, k; add(add(binomial(n-k, n-i)*swing(2*i+1), i=k..n), k=0..n) end:
CROSSREFS
KEYWORD
nonn
AUTHOR
Peter Luschny, Aug 06 2009
STATUS
approved