A320995 Number of connected self-dual nets with 2n nodes.

1, 0, 5, 136, 24162, 29488085, 286615837574, 21717610066598371, 12980514969049888065118, 62082684164458190567999459967, 2405195234525224724112302276711929089, 762399076229936058613587754015434541854738381

Offset: 0

Author

N. J. A. Sloane, Oct 26 2018

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..40
• Edward A. Bender and E. Rodney Canfield, Enumeration of connected invariant graphs, Journal of Combinatorial Theory, Series B 34.3 (1983): 268-278. See p. 275.
• Andrew Howroyd, PARI Program

Crossrefs

Cf. A004103 (not necessarily connected nets), A004107 (self-dual), A320489 (connected nets).

Programs

PARI

\\ See link for program.
A320995seq(15) \\ Andrew Howroyd, Jan 27 2020

Formula

a(2*n-1) = b(2*n-1) - A320489(2*n-1)/2, a(2*n) = b(2*n) - (A320489(2*n)-a(n))/2 where b is the Inverse Euler transform of A004107. - Andrew Howroyd, Jan 27 2020

Extensions

a(0)=1 prepended and terms a(7) and beyond from Andrew Howroyd, Jan 26 2020