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%I A297196 #28 Jan 03 2022 03:29:48
%S A297196 1,1,1,2,6,23,108,601,3863,28159,229524,2068498,20422119,219201032,
%T A297196 2541402277,31651201409,421417326357,5973390936116,89807344973286,
%U A297196 1427447458217437,23916152814768626,421268372668968823
%N A297196 Number of label-increasing forests with branching bounded by 3.
%C A297196 See Riordan 1978 or 1979 for precise definition.
%H A297196 Letong Hong and Rupert Li, <a href="https://arxiv.org/abs/2112.15081">Length-Four Pattern Avoidance in Inversion Sequences</a>, arXiv:2112.15081 [math.CO], 2021.
%H A297196 John Riordan, <a href="/A297196/a297196.pdf">Forests of label-increasing trees</a>, annotated scanned copy of 1978 pre-publication version.
%H A297196 John Riordan, <a href="https://doi.org/10.1002/jgt.3190030204">Forests of label-increasing trees</a>, J. Graph Theory, 3 (1979), 127-133.
%F A297196 E.g.f. F(x) satisfies the ODE: F'(x) = Sum_{j=0..3} (F(x)-1)^j/j! with F(0)=1. - _Max Alekseyev_, Jul 12 2019
%p A297196 Order := 25; F := rhs( dsolve( { diff(y(x), x) = sum((y(x)-1)^j/j!, j=0..3), y(0)=1 }, y(x), type=series ) ); seq( coeff(F, x, n)*n!, n=0..24 ); # _Max Alekseyev_, Jul 12 2019
%t A297196 m = 22; F[_] = 0;
%t A297196 Do[F[x_] = 1 + Integrate[Sum[(F[x] - 1)^j/j!, {j, 0, 3}], x] + O[x]^m // Normal, {m}];
%t A297196 CoefficientList[F[x], x]*Range[0, m-1]! (* _Jean-François Alcover_, Oct 26 2019 *)
%Y A297196 Cf. A297197, A297198, A297200, A297201, A297202, A297203, A297204.
%K A297196 nonn
%O A297196 0,4
%A A297196 _N. J. A. Sloane_, Jan 10 2018
%E A297196 Edited and more terms added by _Max Alekseyev_, Jul 12 2019

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