A217563 Irregular triangular array read by rows. T(n,k) is the number of weakly connected relations on n labeled nodes with k arcs. (n>=0, 0<=k<=n^2)

1, 1, 1, 0, 2, 5, 4, 1, 0, 0, 12, 56, 111, 123, 84, 36, 9, 1, 0, 0, 0, 128, 944, 3264, 7096, 10936, 12687, 11400, 8004, 4368, 1820, 560, 120, 16, 1, 0, 0, 0, 0, 2000, 21104, 109400, 373920, 950725, 1915405, 3168880, 4394760, 5169230, 5188390, 4454000

Offset

0,5

Comments

Row sums = A062738.

Links

Table of n, a(n) for n=0..49.

Formula

E.g.f.: Log[Sum_{n>=0} (1+y)^(n^2) x^n/n!] + 1

Example

1,
1, 1,
0, 2, 5, 4, 1,
0, 0, 12, 56, 111, 123, 84, 36, 9, 1,
0, 0, 0, 128, 944, 3264, 7096, 10936, 12687, 11400, 8004, 4368, 1820, 560, 120, 16, 1

Mathematica

nn=6; s=Sum[(1+y)^(n^2) x^n/n!, {n, 0, nn}]; Range[0, nn]! CoefficientList[Series[ Log[s]+1, {x, 0, nn}], {x, y}] //Grid

Crossrefs

Cf. A062735.

Sequence in context: A324057 A106315 A285295 * A373427 A254881 A100946

Adjacent sequences: A217560 A217561 A217562 * A217564 A217565 A217566

Keyword

nonn,tabf

Author

Geoffrey Critzer, Oct 07 2012

Status

approved