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A297196
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Number of label-increasing forests with branching bounded by 3.
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8
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1, 1, 1, 2, 6, 23, 108, 601, 3863, 28159, 229524, 2068498, 20422119, 219201032, 2541402277, 31651201409, 421417326357, 5973390936116, 89807344973286, 1427447458217437, 23916152814768626, 421268372668968823
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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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FORMULA
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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
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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..3), 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, 3}], x] + O[x]^m // Normal, {m}];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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