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 A297196 Number of label-increasing forests with branching bounded by 3. 8
 1, 1, 1, 2, 6, 23, 108, 601, 3863, 28159, 229524, 2068498, 20422119, 219201032, 2541402277, 31651201409, 421417326357, 5973390936116, 89807344973286, 1427447458217437, 23916152814768626, 421268372668968823 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS See Riordan 1978 or 1979 for precise definition. LINKS John Riordan, Forests of label-increasing trees, annotated scanned copy of 1978 pre-publication version. John Riordan, Forests of label-increasing trees, J. Graph Theory, 3 (1979), 127-133. FORMULA 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 MAPLE 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 MATHEMATICA m = 22; F[_] = 0; Do[F[x_] = 1 + Integrate[Sum[(F[x] - 1)^j/j!, {j, 0, 3}], x] + O[x]^m // Normal, {m}]; CoefficientList[F[x], x]*Range[0, m-1]! (* Jean-François Alcover, Oct 26 2019 *) CROSSREFS Cf. A297197, A297198, A297200, A297201, A297202, A297203, A297204. Sequence in context: A101053 A155857 A071076 * A112501 A093345 A289681 Adjacent sequences:  A297193 A297194 A297195 * A297197 A297198 A297199 KEYWORD nonn AUTHOR N. J. A. Sloane, Jan 10 2018 EXTENSIONS Edited and more terms added by Max Alekseyev, Jul 12 2019 STATUS approved

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Last modified July 12 02:34 EDT 2020. Contains 335658 sequences. (Running on oeis4.)