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0, 1, 4, 9, 21, 45, 104, 233, 549, 1299, 3157, 7739, 19318, 48627, 123865, 317953, 823063, 2144503, 5623754, 14828072, 39299895, 104636888, 279793448, 751065458, 2023443030, 5469566583, 14830871800, 40330829028, 109972410219, 300628862478, 823779631719
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refs;
listen;
history;
text;
internal format)
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OFFSET
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4,3
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COMMENTS
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Number of free trees with n nodes, each node with degree <= n-3. - Robert A. Russell, Jan 25 2023
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LINKS
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FORMULA
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MATHEMATICA
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b[n_, i_, t_, k_] := b[n, i, t, k] = If[i<1, 0, Sum[Binomial[b[i-1, i-1, k, k]
+ j-1, j]* b[n-i*j, i-1, t-j, k], {j, 0, Min[t, n/i]}]];
b[0, i_, t_, k_] = 1;
Join[{0, 1}, Table[m = n - 4;
gf[x_] := 1 + Sum[b[j - 1, j - 1, m, m] x^j, {j, 1, n}];
ci[x_] := SymmetricGroupIndex[m + 1, x] /. x[i_] -> gf[x^i];
SeriesCoefficient[Series[gf[x] - (gf[x]^2 - gf[x^2])/2 + x ci[x],
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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