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A244455 Number of unlabeled rooted trees with n nodes such that the minimal outdegree of inner nodes equals 1. 3
1, 1, 3, 7, 17, 42, 105, 267, 684, 1775, 4639, 12238, 32491, 86859, 233496, 631082, 1713613, 4673455, 12795426, 35159212, 96927479, 268021520, 743188706, 2066071045, 5757360011, 16079027344, 44997313684, 126166307275, 354384737204, 997083779801, 2809751278062 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 2..800

FORMULA

a(n) = A000081(n) - A001678(n+1).

EXAMPLE

a(5) = 7:

  o    o      o      o      o      o      o

  |    |      |     / \    / \     |     /|\

  o    o      o    o   o  o   o    o    o o o

  |    |     / \   |      |   |   /|\   |

  o    o    o   o  o      o   o  o o o  o

  |   / \   |      |

  o  o   o  o      o

  |

  o

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

seq(a(n), n=2..35);

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, 1, 1] - b[n - 1, n - 1, 2, 2]; Table[a[n], {n, 2, 35}] (* Jean-Fran├žois Alcover, Feb 06 2015, after Maple *)

CROSSREFS

Column k=1 of A244454.

Cf. A106640 (the same for ordered rooted trees).

Sequence in context: A086395 A020730 A003440 * A102071 A191627 A178778

Adjacent sequences:  A244452 A244453 A244454 * A244456 A244457 A244458

KEYWORD

nonn

AUTHOR

Joerg Arndt and Alois P. Heinz, Jun 29 2014

STATUS

approved

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Last modified August 8 05:25 EDT 2020. Contains 336290 sequences. (Running on oeis4.)