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A034799 Triangle read by rows: T(n,k) is the number of partially labeled trees with n nodes, k of which are labeled, 0 <= k <= n.

%I A034799 #18 Mar 23 2023 19:28:23
%S A034799 1,1,1,1,1,1,1,2,3,3,2,4,9,16,16,3,9,26,67,125,125,6,20,75,251,680,
%T A034799 1296,1296,11,48,214,888,3135,8716,16807,16807,23,115,612,3023,13155,
%U A034799 47787,134960,262144,262144,47,286,1747,10038,51873,232154,858578,2450309,4782969,4782969
%N A034799 Triangle read by rows: T(n,k) is the number of partially labeled trees with n nodes, k of which are labeled, 0 <= k <= n.
%D A034799 J. Riordan, An Introduction to Combinatorial Analysis, p. 138.
%H A034799 <a href="/index/Tra#trees">Index entries for sequences related to trees</a>
%F A034799 Reference gives generating function.
%F A034799 E.g.f.: r(x,y) - (1/2)*r(x,y)^2 + (1/2)*r(x^2) where r(x,y) is the e.g.f. for A008295 and r(x) is the o.g.f. for A000081. - _Sean A. Irvine_, Sep 04 2020
%e A034799 Triangle begins:
%e A034799   1;
%e A034799   1, 1;
%e A034799   1, 1, 1;
%e A034799   1, 2, 3, 3;
%e A034799   2, 4, 9, 16, 16;
%e A034799   ...
%Y A034799 Columns are A000055, A000081, A000243, A000269, A000485, A000526, A064785.
%Y A034799 Cf. A008295, A034800.
%K A034799 nonn,tabl
%O A034799 0,8
%A A034799 _N. J. A. Sloane_
%E A034799 More terms from _Sean A. Irvine_, Sep 04 2020
%E A034799 Name edited by _Andrew Howroyd_, Mar 23 2023