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A244533
Number of ordered unlabeled rooted trees with n nodes such that the minimal outdegree of inner nodes equals 4.
3
1, 0, 0, 0, 4, 9, 10, 11, 34, 91, 196, 330, 636, 1377, 2976, 6061, 12199, 25186, 52767, 109066, 224964, 467605, 979056, 2042847, 4244986, 8844130, 18527956, 38878929, 81460220, 170576593, 357894472, 752544917, 1583579674, 3332453026, 7016669752, 14790212086
OFFSET
5,5
LINKS
FORMULA
a(n) ~ c * d^n / (sqrt(Pi) * n^(3/2)), where d = 2.18452974131524781307797151868229485574758... is the root of the equation -229 - 36*d + 2*d^2 - 32*d^3 + 19*d^4 + 4*d^5 = 0, and c = 0.181069926661856899940163775713243367029404419526724... . - Vaclav Kotesovec, Jul 02 2014
MAPLE
b:= proc(n, t, k) option remember; `if`(n=0,
`if`(t in [0, k], 1, 0), `if`(t>n, 0, add(b(j-1, k$2)*
b(n-j, max(0, t-1), k), j=1..n)))
end:
a:= n-> b(n-1, 4$2) -b(n-1, 5$2):
seq(a(n), n=5..45);
MATHEMATICA
b[n_, t_, k_] := b[n, t, k] = If[n == 0, If[t == 0 || t == k, 1, 0], If[t > n, 0, Sum[b[j - 1, k, k]*b[n - j, Max[0, t - 1], k], {j, 1, n}]]]; T[n_, k_] := b[n - 1, k, k] - If[n == 1 && k == 0, 0, b[n - 1, k + 1, k + 1]]; a[n_] := b[n - 1, 4, 4] - b[n - 1, 5, 5]; Table[a[n], {n, 5, 45}] (* Jean-François Alcover, Feb 06 2015, after Maple *)
CROSSREFS
Column k=4 of A244530.
Cf. A244458.
Sequence in context: A125726 A352323 A175308 * A180149 A155879 A172192
KEYWORD
nonn
AUTHOR
Joerg Arndt and Alois P. Heinz, Jun 29 2014
STATUS
approved