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A036769
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Number of ordered rooted trees with n non-root nodes and all outdegrees <= seven.
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5
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1, 1, 2, 5, 14, 42, 132, 429, 1429, 4852, 16730, 58422, 206192, 734332, 2635680, 9524301, 34622207, 126520393, 464517300, 1712650520, 6338433840, 23538973950, 87690410580, 327611738790, 1227178265182, 4607940112396, 17341126763366, 65395548619912
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OFFSET
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0,3
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LINKS
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FORMULA
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G.f. A(x) satisfies: A(x) = 1 + Sum_{k=1..7} x^k*A(x)^k. - Ilya Gutkovskiy, May 03 2019
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MAPLE
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r := 7; [ seq((1/n)*add( (-1)^j*binomial(n, j)*binomial(2*n-2-j*(r+1), n-1), j=0..floor((n-1)/(r+1))), n=1..30) ];
# second Maple program:
b:= proc(u, o) option remember; `if`(u+o=0, 1,
add(b(u-j, o+j-1), j=1..min(1, u))+
add(b(u+j-1, o-j), j=1..min(7, o)))
end:
a:= n-> b(0, n):
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MATHEMATICA
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b[u_, o_] := b[u, o] = If[u + o == 0, 1, Sum[b[u - j, o + j - 1], {j, 1, Min[1, u]}] + Sum[b[u + j - 1, o - j], {j, 1, Min[7, o]}]];
a[n_] := b[0, n];
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PROG
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(PARI) a(n)=if(n<0, 0, polcoeff(serreverse(x/sum(k=0, 7, x^k)+O(x^(n+2))), n+1)) /* Ralf Stephan */
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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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