OFFSET
1,2
FORMULA
G.f.: Sum_{n,k} T(n,k)*x^n/n!*y^k=(F(x,y)-1)*exp(F(x,y)-1)=G(x,y)*log(G(x,y)) where G(x,y)=Sum_{n=0..oo} (1+y)^(n(n-1)/2)*x^n/n! and F(x,y)=1+log(G(x,y)) is g.f. of A062734.
EXAMPLE
Triangle begins:
1;
2, 1;
3, 6, 3, 1;
4, 18, 30, 24, 15, 6, 1;
5, 40, 135, 250, 295, 282, 215, 120, 45, 10, 1;
...
T(3,1) = 6 since there are three different subgraphs of K_3 with one edge and each subgraph has two connected components.
PROG
(PARI) { G=sum(n=0, 6, (1+y)^(n*(n-1)/2)*x^n/n!); K=G*log(G); for(n=1, 6, print(Vecrev(n!*polcoeff(K, n, x)))) }
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Max Alekseyev, Nov 23 2006
STATUS
approved