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A244459 Number of unlabeled rooted trees with n nodes such that the minimal outdegree of inner nodes equals 5. 3
1, 0, 0, 0, 0, 1, 2, 2, 2, 2, 4, 7, 12, 16, 21, 29, 43, 65, 99, 142, 206, 297, 436, 641, 945, 1383, 2029, 2976, 4378, 6432, 9464, 13913, 20495, 30205, 44547, 65670, 96846, 142857, 210941, 311636, 460613, 680848, 1006682, 1488915, 2203324, 3261840, 4830671 (list; graph; refs; listen; history; text; internal format)
OFFSET
6,7
LINKS
MAPLE
b:= proc(n, i, t, k) option remember; `if`(n=0, `if`(t in [0, k],
1, 0), `if`(i<1 or t>n, 0, add(binomial(b((i-1)$2, k$2)+j-1, j)*
b(n-i*j, i-1, max(0, t-j), k), j=0..n/i)))
end:
a:= n-> b(n-1$2, 5$2) -b(n-1$2, 6$2):
seq(a(n), n=6..55);
MATHEMATICA
b[n_, i_, t_, k_] := b[n, i, t, k] = If[n == 0, If[t == 0 || t == k, 1, 0], If[i < 1, 0, Sum[Binomial[b[i - 1, i - 1, k, k] + j - 1, j]*b[n - i*j, i - 1, Max[0, t - j], k], {j, 0, n/i}]] // FullSimplify]; a[n_] := b[n - 1, n - 1, 5, 5] - b[n - 1, n - 1, 6, 6]; Table[a[n], {n, 6, 55}] (* Jean-François Alcover, Feb 06 2015, after Maple *)
CROSSREFS
Column k=5 of A244454.
Cf. A244534.
Sequence in context: A060824 A334125 A364811 * A064849 A269302 A132189
KEYWORD
nonn
AUTHOR
Joerg Arndt and Alois P. Heinz, Jun 29 2014
STATUS
approved

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Last modified March 2 07:45 EST 2024. Contains 370460 sequences. (Running on oeis4.)