OFFSET
2,3
COMMENTS
In each such graph: (i) no two nodes of the same color are adjacent, (ii) the colors are interchangeable, and (iii) there must be at least one vertex of each color.
REFERENCES
F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, page 16.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 2..1403 (rows 2..25)
FORMULA
O.g.f. of row n: Sum_{k=0..n-1} binomial(n,k)*(1+x)^(k*(n-k))/2.
EXAMPLE
Triangle begins:
1, 1;
3, 6, 3;
7, 24, 30, 16, 3;
15, 80, 180, 220, 155, 60, 10;
31, 240, 840, 1740, 2340, 2106, 1260, 480, 105, 10;
MATHEMATICA
Flatten[CoefficientList[Expand[Table[Sum[Binomial[n, k] (1 + x)^(k (n - k)), {k, 1, n - 1}]/2!, {n, 1, 7}]], x]]
PROG
(PARI) Row(n) = {Vecrev(sum(k=1, n-1, binomial(n, k)*(1+x)^(k*(n-k))/2))}
{ for(n=2, 8, print(Row(n))) } \\ Andrew Howroyd, Apr 18 2021
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Geoffrey Critzer, Nov 27 2011
EXTENSIONS
Terms a(42) and beyond from Andrew Howroyd, Apr 18 2021
STATUS
approved
