A285641 Triangle read by rows: T(n,k) is the number of hypergraphs on n labeled nodes that have exactly k isolated points, n>=0, 0<=k<=n.

1, 1, 1, 5, 2, 1, 109, 15, 3, 1, 32297, 436, 30, 4, 1, 2147321017, 161485, 1090, 50, 5, 1, 9223372023970362989, 12883926102, 484455, 2180, 75, 6, 1, 170141183460469231667123699502996689125, 64563604167792540923, 45093741357, 1130395, 3815, 105, 7, 1

Offset

0,4

Comments

An isolated point is a vertex of degree 0.

Links

Table of n, a(n) for n=0..35.

Formula

E.g.f.: exp(y*x)*A(x) where A(x) is the e.g.f. for A003465.

Example

Triangle begins:
1,
1, 1,
5, 2, 1,
109, 15, 3, 1,
32297, 436, 30, 4, 1,
2147321017, 161485, 1090, 50, 5, 1
  ...

Mathematica

nn = 5; A[z_] := Sum[Sum[(-1)^i Binomial[n, i] 2^(2^(n - i) - 1), {i, 0, n}] z^n/n!, {n, 0, nn}]; Map[Select[#, # > 0 &] &, Range[0, nn]! CoefficientList[Series[Exp[u z]  A[z], {z, 0, nn}], {z, u}]] // Grid

Crossrefs

Column k=0 is A003465.

Row sums give A058891.

Sequence in context: A229959 A174485 A334343 * A257856 A021661 A324187

Adjacent sequences: A285638 A285639 A285640 * A285642 A285643 A285644

Keyword

nonn,tabl

Author

Geoffrey Critzer, Apr 23 2017

Status

approved