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A297204
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Number of label-increasing forests with branching bounded by 5.
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7
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1, 1, 1, 2, 6, 24, 120, 719, 5017, 39938, 357100, 3542771, 38615127, 458663713, 5896341413, 81562642449, 1207920218823, 19068760619088, 319648589219950, 5670332828427154, 106122789165032548, 2089715042280197113
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OFFSET
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0,4
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COMMENTS
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See Riordan 1978 or 1979 for precise definition.
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LINKS
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Table of n, a(n) for n=0..21.
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.
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FORMULA
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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
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MAPLE
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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
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MATHEMATICA
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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 *)
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CROSSREFS
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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
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane, Jan 10 2018
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EXTENSIONS
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Corrected and extended by Max Alekseyev, Jul 12 2019
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STATUS
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approved
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