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A245126 Number of n-node rooted identity trees with thinning limbs and root outdegree (branching factor) 7.

%I A245126 #7 Jul 12 2014 08:49:02
%S A245126 1,8,26,86,247,669,1709,4251,10214,24066,55551,126369,283505,629261,
%T A245126 1382778,3013846,6519955,14015077,29952488,63690016,134807361,
%U A245126 284170813,596800591,1249172169,2606663357,5424220543,11258470062,23313312932,48171597034,99337649116
%N A245126 Number of n-node rooted identity trees with thinning limbs and root outdegree (branching factor) 7.
%H A245126 Alois P. Heinz, <a href="/A245126/b245126.txt">Table of n, a(n) for n = 25..500</a>
%p A245126 b:= proc(n, i, h, v) option remember; `if`(n=0, `if`(v=0, 1, 0),
%p A245126       `if`(i<1 or v<1 or n<v, 0, add(binomial(A(i, min(i-1, h)), j)
%p A245126        *b(n-i*j, i-1, h, v-j), j=0..min(n/i, v))))
%p A245126     end:
%p A245126 A:= proc(n, k) option remember;
%p A245126       `if`(n<2, n, add(b(n-1$2, j$2), j=1..min(k, n-1)))
%p A245126     end:
%p A245126 a:= n-> b(n-1$2, 7$2):
%p A245126 seq(a(n), n=25..60);
%Y A245126 Column k=7 of A245120.
%K A245126 nonn
%O A245126 25,2
%A A245126 _Alois P. Heinz_, Jul 12 2014