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A304977 Number of unlabeled hyperforests spanning n vertices with singleton edges allowed.

%I A304977 #8 Aug 28 2018 00:27:01
%S A304977 1,1,4,14,55,235,1112,5672,30783,175733,1042812,6385278,40093375,
%T A304977 257031667,1676581863,11098295287,74401300872,504290610004,
%U A304977 3451219615401,23821766422463,165684694539918,1160267446543182,8175446407807625,57928670942338011,412561582740147643
%N A304977 Number of unlabeled hyperforests spanning n vertices with singleton edges allowed.
%H A304977 Andrew Howroyd, <a href="/A304977/b304977.txt">Table of n, a(n) for n = 0..200</a>
%F A304977 Euler transform of b(1) = 1, b(n > 1) = A134959(n).
%e A304977 Non-isomorphic representatives of the a(3) = 14 hyperforests are the following:
%e A304977   {{1,2,3}}
%e A304977   {{3},{1,2}}
%e A304977   {{3},{1,2,3}}
%e A304977   {{1,3},{2,3}}
%e A304977   {{1},{2},{3}}
%e A304977   {{2},{3},{1,3}}
%e A304977   {{2},{3},{1,2,3}}
%e A304977   {{3},{1,2},{2,3}}
%e A304977   {{3},{1,3},{2,3}}
%e A304977   {{1},{2},{3},{2,3}}
%e A304977   {{1},{2},{3},{1,2,3}}
%e A304977   {{2},{3},{1,2},{1,3}}
%e A304977   {{2},{3},{1,3},{2,3}}
%e A304977   {{1},{2},{3},{1,3},{2,3}}
%o A304977 (PARI) \\ here b(n) is A318494 as vector
%o A304977 EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}
%o A304977 b(n)={my(v=[1]); for(i=2, n, v=concat([1], EulerT(EulerT(2*v)))); v}
%o A304977 seq(n)={my(u=2*b(n)); concat([1], EulerT(Vec(Ser(EulerT(u))*(1-x*Ser(u))-1)))} \\ _Andrew Howroyd_, Aug 27 2018
%Y A304977 Cf. A030019, A035053, A134954, A134955, A134956, A134957, A134958, A134959, A144959, A304867, A304911, A304912, A304918.
%K A304977 nonn
%O A304977 0,3
%A A304977 _Gus Wiseman_, May 22 2018
%E A304977 Terms a(7) and beyond from _Andrew Howroyd_, Aug 27 2018