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.

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

Offset: 1

Author

Max Alekseyev, Jan 09 2007

Keywords

• sign
• tabf

Comments

Row-reversed version of A125210, see A125210 for further details.

Examples

			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;
   ...
		

Crossrefs

Cf. A125210 (row-reversed version), A125209 (dual version).

Programs

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)))) }