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 A141610 Number of rooted trees with n points and exactly k specified colors: C(n,k), 0
 1, 1, 2, 2, 10, 9, 4, 44, 102, 64, 9, 196, 870, 1304, 625, 20, 876, 6744, 18200, 20080, 7776, 48, 4020, 50421, 218260, 416500, 362322, 117649, 115, 18766, 371676, 2427600, 7133655, 10465290, 7503328, 2097152, 286, 89322, 2731569, 25919692 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS The number of rooted trees with n points having any of c colors is Sum_k C(n,k) {c choose k}. LINKS Andrew Howroyd, Table of n, a(n) for n = 1..1275 J. Riordan, The numbers of labeled colored and chromatic trees, Acta Mathematica, 97 (1957), 211-225. J. Riordan, The numbers of labeled colored and chromatic trees. EXAMPLE C(n,1) is the number of rooted trees with n points (A000081). C(n,n)=n^{n-1}. C(3,2)=10 is the number of rooted trees with three points and two colors: AAB, ABB, ABA, BAA, BAB, BBA, A(BB), A(AB), B(AA), B(AB), where ABC is a rooted tree with A the root, B attached to A and C; A(BC) is a rooted tree with A the root, A attached to B and C.    1;    1,   2;    2,  10,    9;    4,  44,  102,    64;    9, 196,  870,  1304,   625;   20, 876, 6744, 18200, 20080, 7776;   ... MATHEMATICA p[a_List]:=a; p[a_List, b_List, c___List]:=If[Length[a] <=Length[b], p[PadRight[a, Length[b]]+b, c], p[b, a, c]]; c[i_, j_]:=If[i

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Last modified April 4 07:32 EDT 2020. Contains 333213 sequences. (Running on oeis4.)