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A245750
Number of identity trees with n nodes where the maximal outdegree (branching factor) equals 5.
2
1, 7, 26, 91, 291, 885, 2588, 7373, 20555, 56413, 152812, 409696, 1089029, 2874506, 7542257, 19690939, 51188137, 132579401, 342294012, 881292334, 2263535926, 5801350565, 14840644204, 37901021924, 96650247055, 246137463494, 626087267035, 1590840361215
OFFSET
15,2
LINKS
MAPLE
b:= proc(n, i, t, k) option remember; `if`(n=0, 1,
`if`(i<1, 0, add(binomial(b(i-1$2, k$2), j)*
b(n-i*j, i-1, t-j, k), j=0..min(t, n/i))))
end:
a:= n-> b(n-1$2, 5$2) -b(n-1$2, 4$2):
seq(a(n), n=15..60);
MATHEMATICA
b[n_, i_, t_, k_] := b[n, i, t, k] = If[n == 0, 1, If[i<1, 0, Sum[Binomial[ b[i-1, i-1, k, k], j]*b[n - i*j, i-1, t-j, k], {j, 0, Min[t, n/i]}]]];
a[n_] := b[n-1, n-1, 5, 5] - b[n-1, n-1, 4, 4];
Table[a[n], {n, 15, 60}] (* Jean-François Alcover, Aug 28 2021, after Maple code *)
CROSSREFS
Column k=5 of A244523.
Sequence in context: A240256 A372611 A279761 * A268776 A050476 A026617
KEYWORD
nonn
AUTHOR
Joerg Arndt and Alois P. Heinz, Jul 31 2014
STATUS
approved