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A323817 Number of connected set-systems covering n vertices with no singletons. 5
1, 0, 1, 12, 1990, 67098648, 144115187673201808, 1329227995784915871895000743748659792, 226156424291633194186662080095093570015284114833799899656335137245499581360 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

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

FORMULA

Logarithmic transform of A323816.

EXAMPLE

The a(3) = 12 set-systems:

  {{1,2,3}}

  {{1,2},{1,3}}

  {{1,2},{2,3}}

  {{1,3},{2,3}}

  {{1,2},{1,2,3}}

  {{1,3},{1,2,3}}

  {{2,3},{1,2,3}}

  {{1,2},{1,3},{2,3}}

  {{1,2},{1,3},{1,2,3}}

  {{1,2},{2,3},{1,2,3}}

  {{1,3},{2,3},{1,2,3}}

  {{1,2},{1,3},{2,3},{1,2,3}}

The A323816(4) - a(4) = 3 disconnected set-systems covering n vertices with no singletons:

  {{1,2},{3,4}}

  {{1,3},{2,4}}

  {{1,4},{2,3}}

MAPLE

b:= n-> add(2^(2^(n-j)-n+j-1)*binomial(n, j)*(-1)^j, j=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=10;

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

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

CROSSREFS

Cf. A001187, A016031, A048143, A092918, A293510, A317795, A323816 (not necessarily connected), A323818 (with singletons), A323819, A323820 (unlabeled case).

Sequence in context: A326601 A265216 A011920 * A263584 A323816 A208252

Adjacent sequences:  A323814 A323815 A323816 * A323818 A323819 A323820

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jan 30 2019

STATUS

approved

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Last modified March 4 14:32 EST 2021. Contains 341794 sequences. (Running on oeis4.)