A122067 a(n) = 2^A014105(n).

1, 8, 1024, 2097152, 68719476736, 36028797018963968, 302231454903657293676544, 40564819207303340847894502572032, 87112285931760246646623899502532662132736, 2993155353253689176481146537402947624255349848014848

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

Table of n, a(n) for n=0..9.

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

Cf. A006125, A014105.

Sequence in context: A291831 A085533 A360773 * A076688 A004808 A320981

Adjacent sequences: A122064 A122065 A122066 * A122068 A122069 A122070

Keyword

nonn

Author

Benoit Cloitre, Oct 15 2006

Status

approved