cp's OEIS Frontend

A127258 Irregular triangle read by rows: B(n,k) (n>=1, 0<=k<=n(n-1)/2) is such that SUM B(n,k)*q^(n*(n-1)/2-k) 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.

%I A127258 #11 Mar 13 2022 19:02:47
%S A127258 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,
%T A127258 -24,270,-1350,3925,-7260,8712,-6485,2445,60,-330,-18,45,20,0,-15,6,
%U A127258 120,-2016,15750,-75810,250950,-603435,1084104,-1471305,1502550,-1128820,589281,-182721
%N A127258 Irregular triangle read by rows: B(n,k) (n>=1, 0<=k<=n(n-1)/2) is such that SUM B(n,k)*q^(n*(n-1)/2-k) 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.
%C A127258 Row-reversed version of A125210, see A125210 for further details.
%e A127258 Triangle begins:
%e A127258    1;
%e A127258   -1,  2;
%e A127258    1,  0,   -3,   3;
%e A127258    2, -6,    3,   4,   0,  -6,  4;
%e A127258   -6, 40, -105, 130, -60, -18, 15, 10, 0, -10, 5;
%e A127258    ...
%o A127258 (PARI) { H=sum(n=0, 6, x^n/(1-q)^(n*(n-1)/2)/n!); B=H*log(H); for(n=1, 6, print(Vec((1-q)^(n*(n-1)/2)*n!*polcoeff(B, n, x)))) }
%Y A127258 Cf. A125210 (row-reversed version), A125209 (dual version).
%K A127258 sign,tabf
%O A127258 1,3
%A A127258 _Max Alekseyev_, Jan 09 2007