

A125205


Triangular array T(n,k) (n>=1, 0<=k<=n(n1)/2) giving the total number of connected components in all subgraphs (V,E') with E'=k of the complete labeled graph K_n=(V,E).


5



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, 6, 75, 420, 1385, 3015, 4800, 6365, 7170, 6705, 5065, 3009, 1365, 455, 105, 15, 1, 7, 126, 1050, 5355, 18690, 47880, 96796, 166890, 251370, 329945, 373947, 362292, 297115
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OFFSET

1,2


LINKS

Table of n, a(n) for n=1..54.


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(n1)/2)*x^n/n! and F(x,y)=1+log(G(x,y)) is g.f. of A062734.


EXAMPLE

The array starts with
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*(n1)/2)*x^n/n!); K=G*log(G); for(n=1, 6, print(Vecrev(n!*polcoeff(K, n, x)))) }


CROSSREFS

Cf. A062734.
Cf. A125206 (rowreversed version), A125207 (row sums).
Sequence in context: A006895 A202204 A289815 * A125206 A221918 A193897
Adjacent sequences: A125202 A125203 A125204 * A125206 A125207 A125208


KEYWORD

nonn,tabf


AUTHOR

Max Alekseyev, Nov 23 2006


STATUS

approved



