OFFSET
0,2
COMMENTS
a(n) is the number of simple labeled graphs on 2(n+1) nodes such that every vertex has odd degree. The complements of these graphs are precisely the Eulerian graphs on 2(n+1) nodes. a(1) = 8 because we have: K_4; K_1,3; and K_2 + K_2 with 1,4, and 3 labelings respectively: 1 + 4 + 3 = 8. Cf. A006125. - Geoffrey Critzer, Feb 16 2020
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..40
FORMULA
a(n) = (-1)^floor(n/2)/Product_{i=1..2*n} cos(i*Pi/(2*n+1))^i.
MAPLE
a:= n-> 2^(n*(2*n+1)):
seq(a(n), n=0..10); # Alois P. Heinz, Feb 16 2020
MATHEMATICA
Table[2^(Binomial[n, 2] - (n - 1)), {n, 2, 20, 2}] (* Geoffrey Critzer, Feb 16 2020 *)
PROG
(PARI) a(n)=2^(n*(2*n+1))
CROSSREFS
KEYWORD
nonn
AUTHOR
Benoit Cloitre, Oct 15 2006
STATUS
approved