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A244460 Number of unlabeled rooted trees with n nodes such that the minimal outdegree of inner nodes equals 6. 3
1, 0, 0, 0, 0, 0, 1, 2, 2, 2, 2, 2, 4, 7, 12, 16, 21, 25, 34, 47, 70, 103, 147, 201, 276, 377, 527, 743, 1057, 1486, 2088, 2911, 4073, 5704, 8027, 11290, 15897, 22340, 31411, 44159, 62165, 87516, 123296, 173642, 244636, 344684, 485976, 685362, 966971, 1364301 (list; graph; refs; listen; history; text; internal format)
OFFSET

7,8

LINKS

Alois P. Heinz, Table of n, a(n) for n = 7..900

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, 6$2) -b(n-1$2, 7$2):

seq(a(n), n=7..60);

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, 6, 6] - b[n - 1, n - 1, 7, 7]; Table[a[n], {n, 7, 60}] (* Jean-Fran├žois Alcover, Feb 06 2015, after Maple *)

CROSSREFS

Column k=6 of A244454.

Cf. A244535.

Sequence in context: A175732 A168260 A008737 * A160419 A152659 A180214

Adjacent sequences:  A244457 A244458 A244459 * A244461 A244462 A244463

KEYWORD

nonn

AUTHOR

Joerg Arndt and Alois P. Heinz, Jun 29 2014

STATUS

approved

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Last modified February 22 20:03 EST 2019. Contains 320403 sequences. (Running on oeis4.)