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%I #39 Dec 18 2016 01:22:41
%S 1,1,1,1,1,1,1,2,2,2,1,2,4,4,2,1,3,6,10,8,4,1,3,9,17,22,15,6,1,4,12,
%T 30,47,53,32,11,1,4,16,44,91,127,121,66,18,1,5,20,67,158,282,346,292,
%U 142,37,1,5,25,91,258,539,841,921,688,306,66,1,6,30,126,397,978,1804,2498,2456,1662,672,135,1,6,36,163,588,1636,3550,5856,7260,6489,3978,1483,265,1,7,42,213,838,2638,6495,12554,18636,20946,17082,9629,3316,552,1,8
%N Number T(m,n) of series-reduced free trees with n nodes of which exactly m >= 3 are leaves, m+1 <= n <= 2m-2.
%C The sequence of row sums a(m) = Sum_{n} T(m,n) is A007827.
%C The sequence of column sums a(n) = Sum_{m} T(m,n) is A000014.
%H Stephan Beyer, <a href="https://gist.github.com/sbeyer/bb2731d4113d3da62dd8b44c262e9fc1">Python code to generate the sequence on GitHub Gist</a>
%e m\n | 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
%e -------------------------------------------------------
%e 3 | . 1 . . . . . . . . . . . . . . . .
%e 4 | . . 1 1 . . . . . . . . . . . . . .
%e 5 | . . . 1 1 1 . . . . . . . . . . . .
%e 6 | . . . . 1 2 2 2 . . . . . . . . . .
%e 7 | . . . . . 1 2 4 4 2 . . . . . . . .
%e 8 | . . . . . . 1 3 6 10 8 4 . . . . . .
%e 9 | . . . . . . . 1 3 9 17 22 15 6 . . . .
%e 10 | . . . . . . . . 1 4 12 30 47 53 32 11 . .
%e 11 | . . . . . . . . . 1 4 16 44 91 127 121 66 18
%Y Cf. A000014, A007827.
%Y Transpose of A271362.
%K nonn,tabf
%O 3,8
%A _Stephan Beyer_, Apr 01 2016
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