A320993 - OEIS

%I #12 Jan 27 2020 17:33:47

%S 1,1,6,81,2796,285205,96322648,112087066485,458071927263177,

%T 6665704296474517580,349377209492189224235030,

%U 66602723163954143548104716149,46557323273646194397454383970079368,120168498151800396724425771086539073209571,1152049915423012273792614840558950392103437052846

%N Number of connected self-dual marked graphs on 2n nodes.

%H Andrew Howroyd, <a href="/A320993/b320993.txt">Table of n, a(n) for n = 0..50</a>

%H Edward A. Bender and E. Rodney Canfield, <a href="https://doi.org/10.1016/0095-8956(83)90040-0">Enumeration of connected invariant graphs</a>, Journal of Combinatorial Theory, Series B 34.3 (1983): 268-278. See p. 274.

%H Andrew Howroyd, <a href="/A320993/a320993_1.txt">PARI Program</a>

%F a(2*n-1) = b(2*n-1) - A054921(2*n-1)/2, a(2*n) = b(2*n) - (A054921(2*n)-a(n))/2 where b is the Inverse Euler transform of A000595. - _Andrew Howroyd_, Jan 27 2020

%o (PARI) \\ See link for program.

%o A320993seq(15) \\ _Andrew Howroyd_, Jan 27 2020

%Y Cf. A000666 (not necessarily connected marked graphs), A000595 (self dual on 2n nodes), A054921 (connected marked graphs).

%K nonn

%O 0,3

%A _N. J. A. Sloane_, Oct 26 2018

%E a(0)=1 prepended and terms a(7) and beyond from _Andrew Howroyd_, Jan 26 2020