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 A297204 Number of label-increasing forests with branching bounded by 5. 7
 1, 1, 1, 2, 6, 24, 120, 719, 5017, 39938, 357100, 3542771, 38615127, 458663713, 5896341413, 81562642449, 1207920218823, 19068760619088, 319648589219950, 5670332828427154, 106122789165032548, 2089715042280197113 (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..5} (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..5), 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, 5}], x] + O[x]^m // Normal, {m}]; CoefficientList[F[x], x]*Range[0, m - 1]! (* Jean-François Alcover, Oct 26 2019 *) CROSSREFS Cf. A297196, A297197, A297198, A297200, A297201, A297202, A297203. Sequence in context: A248838 A052398 A047890 * A071088 A177533 A122417 Adjacent sequences: A297201 A297202 A297203 * A297205 A297206 A297207 KEYWORD nonn AUTHOR N. J. A. Sloane, Jan 10 2018 EXTENSIONS Corrected and extended by Max Alekseyev, Jul 12 2019 STATUS approved

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Last modified December 3 17:09 EST 2022. Contains 358535 sequences. (Running on oeis4.)