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A304977 Number of unlabeled hyperforests spanning n vertices with singleton edges allowed. 1
1, 1, 4, 14, 55, 235, 1112, 5672, 30783, 175733, 1042812, 6385278, 40093375, 257031667, 1676581863, 11098295287, 74401300872, 504290610004, 3451219615401, 23821766422463, 165684694539918, 1160267446543182, 8175446407807625, 57928670942338011, 412561582740147643 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..200

FORMULA

Euler transform of b(1) = 1, b(n > 1) = A134959(n).

EXAMPLE

Non-isomorphic representatives of the a(3) = 14 hyperforests are the following:

  {{1,2,3}}

  {{3},{1,2}}

  {{3},{1,2,3}}

  {{1,3},{2,3}}

  {{1},{2},{3}}

  {{2},{3},{1,3}}

  {{2},{3},{1,2,3}}

  {{3},{1,2},{2,3}}

  {{3},{1,3},{2,3}}

  {{1},{2},{3},{2,3}}

  {{1},{2},{3},{1,2,3}}

  {{2},{3},{1,2},{1,3}}

  {{2},{3},{1,3},{2,3}}

  {{1},{2},{3},{1,3},{2,3}}

PROG

(PARI) \\ here b(n) is A318494 as vector

EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}

b(n)={my(v=[1]); for(i=2, n, v=concat([1], EulerT(EulerT(2*v)))); v}

seq(n)={my(u=2*b(n)); concat([1], EulerT(Vec(Ser(EulerT(u))*(1-x*Ser(u))-1)))} \\ Andrew Howroyd, Aug 27 2018

CROSSREFS

Cf. A030019, A035053, A134954, A134955, A134956, A134957, A134958, A134959, A144959, A304867, A304911, A304912, A304918.

Sequence in context: A088655 A302288 A149490 * A143406 A329777 A323787

Adjacent sequences:  A304974 A304975 A304976 * A304978 A304979 A304980

KEYWORD

nonn

AUTHOR

Gus Wiseman, May 22 2018

EXTENSIONS

Terms a(7) and beyond from Andrew Howroyd, Aug 27 2018

STATUS

approved

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Last modified June 2 18:09 EDT 2020. Contains 334787 sequences. (Running on oeis4.)