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A285616 Triangle read by rows: T(n,k) is the number of hypergraphs on n labeled vertices with exactly k connected components, n>=1, 1<=k<=n. 0
2, 4, 4, 96, 24, 8, 31840, 816, 96, 16, 2147156736, 322240, 4320, 320, 32, 9223372011084915712, 25767883392, 1957440, 18240, 960, 64, 170141183460469231602560095199828453376, 129127208335656968192, 180389362944, 9251200, 67200, 2688, 128 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..28.

FORMULA

E.g.f.: A(x)^y where A(x) = Sum_{n>=0} 2^(2^n-1)x^n/n!.

EXAMPLE

Triangle begins:

2,

4, 4,

96, 24, 8,

31840, 816, 96, 16,

2147156736, 322240, 4320, 320, 32,

9223372011084915712, 25767883392, 1957440, 18240, 960, 64,

...

MATHEMATICA

nn = 6; A[z_] := Sum[2^(2^n - 1) z^n/n!, {n, 0, nn}];

Map[Select[#, # > 0 &] &, Drop[Range[0, nn]! CoefficientList[

     Series[(A[z]^u), {z, 0, nn}], {z, u}], 1]] // Grid

CROSSREFS

Row sums give A058891.

Column 1 is A092918.

Sequence in context: A280795 A059052 A292017 * A065975 A089420 A198505

Adjacent sequences:  A285613 A285614 A285615 * A285617 A285618 A285619

KEYWORD

nonn,tabl

AUTHOR

Geoffrey Critzer, Apr 22 2017

STATUS

approved

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Last modified November 25 20:42 EST 2020. Contains 338627 sequences. (Running on oeis4.)