%I #18 Mar 23 2023 19:28:23

%S 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 1296,1296,11,48,214,888,3135,8716,16807,16807,23,115,612,3023,13155,

%U 47787,134960,262144,262144,47,286,1747,10038,51873,232154,858578,2450309,4782969,4782969

%N 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 J. Riordan, An Introduction to Combinatorial Analysis, p. 138.

%H <a href="/index/Tra#trees">Index entries for sequences related to trees</a>

%F Reference gives generating function.

%F 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 Triangle begins:

%e 1;

%e 1, 1;

%e 1, 1, 1;

%e 1, 2, 3, 3;

%e 2, 4, 9, 16, 16;

%e ...

%Y Columns are A000055, A000081, A000243, A000269, A000485, A000526, A064785.

%Y Cf. A008295, A034800.

%K nonn,tabl

%O 0,8

%A _N. J. A. Sloane_

%E More terms from _Sean A. Irvine_, Sep 04 2020

%E Name edited by _Andrew Howroyd_, Mar 23 2023