cp's OEIS Frontend

A125209 Irregular triangle read by rows: T(n,k) (n>=1, 0<=k<=n(n-1)/2) is such that Sum_k T(n,k)*p^(n*(n-1)/2-k) gives the expectation of the number of connected components after deleting every edge of the complete graph on n labeled vertices with probability p.

%I A125209 #17 Mar 13 2022 19:02:17
%S A125209 1,1,1,-1,3,0,1,2,-6,3,4,0,0,1,-6,20,-15,-10,10,0,5,0,0,0,1,24,-90,90,
%T A125209 25,-60,0,-5,15,0,0,6,0,0,0,0,1,-120,504,-630,0,420,-105,0,-105,0,35,
%U A125209 -21,21,0,0,0,7,0,0,0,0,0,1,720,-3360,5040,-1176,-3150,1680,140,560,-210,-280,112
%N A125209 Irregular triangle read by rows: T(n,k) (n>=1, 0<=k<=n(n-1)/2) is such that Sum_k T(n,k)*p^(n*(n-1)/2-k) gives the expectation of the number of connected components after deleting every edge of the complete graph on n labeled vertices with probability p.
%C A125209 Row-reversed version of A125208, see A125208 for further details.
%e A125209 Triangle begins:
%e A125209    1;
%e A125209    1,  1;
%e A125209   -1,  3,   0,   1;
%e A125209    2, -6,   3,   4,  0, 0, 1;
%e A125209   -6, 20, -15, -10, 10, 0, 5, 0, 0, 0, 1;
%e A125209   ...
%Y A125209 Cf. A125208 (row-reversed version), A127258 (dual version).
%K A125209 sign,tabf
%O A125209 1,5
%A A125209 _Max Alekseyev_, Jan 09 2007