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 A244530 Number T(n,k) of ordered unlabeled rooted trees with n nodes such that the minimal outdegree of inner nodes equals k; triangle T(n,k), n>=1, 0<=k<=n-1, read by rows. 11
 1, 0, 1, 0, 1, 1, 0, 4, 0, 1, 0, 11, 2, 0, 1, 0, 36, 5, 0, 0, 1, 0, 117, 11, 3, 0, 0, 1, 0, 393, 28, 7, 0, 0, 0, 1, 0, 1339, 78, 8, 4, 0, 0, 0, 1, 0, 4630, 201, 21, 9, 0, 0, 0, 0, 1, 0, 16193, 532, 55, 10, 5, 0, 0, 0, 0, 1, 0, 57201, 1441, 121, 11, 11, 0, 0, 0, 0, 0, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,8 COMMENTS T(1,0) = 1 by convention. LINKS Alois P. Heinz, Rows n = 1..141, flattened EXAMPLE T(5,1) = 11: o   o     o     o     o     o     o     o     o     o     o |   |     |     |    / \   / \   / \    |    /|\   /|\   /|\ o   o     o     o   o   o o   o o   o   o   o o o o o o o o o |   |    / \   / \  |         | |   |  /|\  |       |       | o   o   o   o o   o o         o o   o o o o o       o       o |  / \  |         | |         | o o   o o         o o         o | o Triangle T(n,k) begins: 1; 0,     1; 0,     1,   1; 0,     4,   0,  1; 0,    11,   2,  0,  1; 0,    36,   5,  0,  0, 1; 0,   117,  11,  3,  0, 0, 1; 0,   393,  28,  7,  0, 0, 0, 1; 0,  1339,  78,  8,  4, 0, 0, 0, 1; 0,  4630, 201, 21,  9, 0, 0, 0, 0, 1; 0, 16193, 532, 55, 10, 5, 0, 0, 0, 0, 1; MAPLE b:= proc(n, t, k) option remember; `if`(n=0,       `if`(t in [0, k], 1, 0), `if`(t>n, 0, add(b(j-1, k\$2)*        b(n-j, max(0, t-1), k), j=1..n)))     end: T:= (n, k)-> b(n-1, k\$2) -`if`(n=1 and k=0, 0, b(n-1, k+1\$2)): seq(seq(T(n, k), k=0..n-1), n=1..14); MATHEMATICA b[n_, t_, k_] := b[n, t, k] = If[n == 0, If[t == 0 || t == k, 1, 0], If[t>n, 0, Sum[b[j-1, k, k]*b[n-j, Max[0, t-1], k], {j, 1, n}]]]; T[n_, k_] := b[n-1, k, k] - If[n == 1 && k == 0, 0, b[n-1, k+1, k+1]]; Table[Table[T[n, k], {k, 0, n-1}], {n, 1, 14}] // Flatten (* Jean-François Alcover, Jan 13 2015, translated from Maple *) CROSSREFS Columns k=0-10 give: A000007(n-1), A106640(n-2), A244531, A244532, A244533, A244534, A244535, A244536, A244537, A244538, A244539. Row sums give A000108(n-1). Cf. A244454 (unordered unlabeled rooted trees). Sequence in context: A271423 A019974 A046781 * A271424 A117435 A282252 Adjacent sequences:  A244527 A244528 A244529 * A244531 A244532 A244533 KEYWORD nonn,tabl AUTHOR Joerg Arndt and Alois P. Heinz, Jun 29 2014 STATUS approved

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