

A127258


Irregular triangle read by rows: B(n,k) (n>=1, 0<=k<=n(n1)/2) is such that SUM B(n,k)*q^(n*(n1)/2k) gives the expectation of the number of connected components in a random graph on n labeled vertices where every edge is present with probability q.


2



1, 1, 2, 1, 0, 3, 3, 2, 6, 3, 4, 0, 6, 4, 6, 40, 105, 130, 60, 18, 15, 10, 0, 10, 5, 24, 270, 1350, 3925, 7260, 8712, 6485, 2445, 60, 330, 18, 45, 20, 0, 15, 6, 120, 2016, 15750, 75810, 250950, 603435, 1084104, 1471305, 1502550, 1128820, 589281, 182721
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OFFSET

1,3


COMMENTS



LINKS



EXAMPLE

Triangle begins:
1;
1, 2;
1, 0, 3, 3;
2, 6, 3, 4, 0, 6, 4;
6, 40, 105, 130, 60, 18, 15, 10, 0, 10, 5;
...


PROG

(PARI) { H=sum(n=0, 6, x^n/(1q)^(n*(n1)/2)/n!); B=H*log(H); for(n=1, 6, print(Vec((1q)^(n*(n1)/2)*n!*polcoeff(B, n, x)))) }


CROSSREFS



KEYWORD

sign,tabf


AUTHOR



STATUS

approved



