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A318520 Number of unlabeled rooted identity trees with n non-binary nodes. 2

%I #7 Aug 28 2018 18:04:36

%S 0,1,1,1,1,1,1,2,3,5,8,14,23,40,69,122,215,382,679,1217,2185,3944,

%T 7136,12958,23578,43026,78673,144190,264755,487074,897549,1656697,

%U 3062423,5669110,10508397,19503447,36240898,67418514,125551221,234047825,436722486

%N Number of unlabeled rooted identity trees with n non-binary nodes.

%H Alois P. Heinz, <a href="/A318520/b318520.txt">Table of n, a(n) for n = 0..3501</a>

%e a(8) = 3: o o o

%e | | /|\

%e o o o o o

%e | /|\ | |

%e o o o o o o

%e | | | |

%e o o o o

%e | | |

%e o o o

%e |

%e o

%e |

%e o

%e |

%e o

%p b:= proc(n, i, t) option remember; `if`(n=0, `if`(t=1, 0, 1), `if`(i<1, 0,

%p add(b(n-i*j, i-1, max(0, t-j))*binomial(a(i), j), j=0..n/i)))

%p end:

%p a:= n-> `if`(n<2, n, b(n-1$2, 3)):

%p seq(a(n), n=0..50);

%Y Cf. A000081, A004111, A303023.

%K nonn

%O 0,8

%A _Alois P. Heinz_, Aug 28 2018

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)