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A323818 Number of connected set-systems covering n vertices. 34
1, 1, 4, 96, 31840, 2147156736, 9223372011084915712, 170141183460469231602560095199828453376, 57896044618658097711785492504343953923912733397452774312021795134847892828160 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Unlike the nearly identical sequence A092918, this sequence does not count under a(1) the a single-vertex hypergraph with no edges.

LINKS

Table of n, a(n) for n=0..8.

FORMULA

E.g.f.: 1 - x + log(Sum_{n >= 0} 2^(2^n-1) * x^n/n!).

Logarithmic transform of A003465.

EXAMPLE

The a(2) = 4 set-systems:

  {{1,2}}

  {{1},{1,2}}

  {{2},{1,2}}

  {{1},{2},{1,2}}

MAPLE

b:= n-> add(binomial(n, k)*2^(2^(n-k)-1)*(-1)^k, k=0..n):

a:= proc(n) option remember; b(n)-`if`(n=0, 0, add(

       k*binomial(n, k)*b(n-k)*a(k), k=1..n-1)/n)

    end:

seq(a(n), n=0..8);  # Alois P. Heinz, Jan 30 2019

MATHEMATICA

nn=8;

ser=Sum[2^(2^n-1)*x^n/n!, {n, 0, nn}];

Table[SeriesCoefficient[1-x+Log[ser], {x, 0, n}]*n!, {n, 0, nn}]

CROSSREFS

Cf. A001187, A003465 (not necessarily connected), A016031, A048143, A092918, A293510, A317672, A323816, A323817 (no singletons), A323819 (unlabeled case).

Sequence in context: A098695 A307934 A059201 * A027638 A309483 A333539

Adjacent sequences:  A323815 A323816 A323817 * A323819 A323820 A323821

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jan 30 2019

STATUS

approved

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Last modified May 30 17:22 EDT 2020. Contains 334728 sequences. (Running on oeis4.)