OFFSET
1,4
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..174
Eric Weisstein's World of Mathematics, Complete Tripartite Graph
Wikipedia, Chromatic Polynomial
FORMULA
a(n) = 1/(2*n) * Sum_{j,m=1..n} S2(n,j) * S2(n,m) * (n-j-m)^n * Product_{i=0..j+m-1} (n-i) with S2 = A008277.
a(n) = A212221(n,n).
a(n) ~ c * d^n * n!^3 / n^(5/2), where d = 2.1534859143209968... and c = 0.008659981748969... . - Vaclav Kotesovec, Feb 18 2017
MAPLE
a:= n-> add(add(Stirling2(n, k)*Stirling2(n, m)*
mul(n-i, i=0..k+m-1)*(n-k-m)^n, m=1..n), k=1..n)/(2*n):
seq(a(n), n=1..20);
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Feb 09 2017
STATUS
approved