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.

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, 25, -60, 0, -5, 15, 0, 0, 6, 0, 0, 0, 0, 1, -120, 504, -630, 0, 420, -105, 0, -105, 0, 35, -21, 21, 0, 0, 0, 7, 0, 0, 0, 0, 0, 1, 720, -3360, 5040, -1176, -3150, 1680, 140, 560, -210, -280, 112

Offset

1,5

Comments

Row-reversed version of A125208, see A125208 for further details.

Links

Table of n, a(n) for n=1..74.

Example

Triangle begins:
   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;
  ...

Crossrefs

Cf. A125208 (row-reversed version), A127258 (dual version).

Sequence in context: A273901 A014573 A067166 * A356517 A263313 A071818

Adjacent sequences: A125206 A125207 A125208 * A125210 A125211 A125212

Keyword

sign,tabf

Author

Max Alekseyev, Jan 09 2007

Status

approved