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 A292086 Number T(n,k) of (unlabeled) rooted trees with n leaf nodes and without unary nodes such that k is the maximum of 1 and the node outdegrees; triangle T(n,k), n>=1, 1<=k<=n, read by rows. 12
 1, 0, 1, 0, 1, 1, 0, 2, 2, 1, 0, 3, 6, 2, 1, 0, 6, 17, 7, 2, 1, 0, 11, 47, 22, 7, 2, 1, 0, 23, 133, 72, 23, 7, 2, 1, 0, 46, 380, 230, 77, 23, 7, 2, 1, 0, 98, 1096, 751, 256, 78, 23, 7, 2, 1, 0, 207, 3186, 2442, 861, 261, 78, 23, 7, 2, 1, 0, 451, 9351, 8006, 2897, 887, 262, 78, 23, 7, 2, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,8 LINKS Alois P. Heinz, Rows n = 1..141, flattened FORMULA T(n,k) = A292085(n,k) - A292085(n,k-1) for k>2, T(n,1) = A292085(n,1). EXAMPLE :   T(4,2) = 2        :   T(4,3) = 2      : T(4,4) = 1 : :                     :                   :            : :       o       o     :      o       o    :     o      : :      / \     / \    :     / \     /|\   :   /( )\    : :     o   N   o   o   :    o   N   o N N  :  N N N N   : :    / \     ( ) ( )  :   /|\     ( )     :            : :   o   N    N N N N  :  N N N    N N     :            : :  ( )                :                   :            : :  N N                :                   :            : :                     :                   :            : Triangle T(n,k) begins:   1;   0,  1;   0,  1,   1;   0,  2,   2,   1;   0,  3,   6,   2,  1;   0,  6,  17,   7,  2,  1;   0, 11,  47,  22,  7,  2, 1;   0, 23, 133,  72, 23,  7, 2, 1;   0, 46, 380, 230, 77, 23, 7, 2, 1; MAPLE b:= proc(n, i, v, k) option remember; `if`(n=0,       `if`(v=0, 1, 0), `if`(i<1 or v<1 or n A(n, k)-`if`(k=1, 0, A(n, k-1)): seq(seq(T(n, k), k=1..n), n=1..15); MATHEMATICA b[n_, i_, v_, k_] := b[n, i, v, k] = If[n == 0, If[v == 0, 1, 0], If[i < 1 || v < 1 || n < v, 0, If[v == n, 1, Sum[Binomial[A[i, k] + j - 1, j]*b[n - i*j, i - 1, v - j, k], {j, 0, Min[n/i, v]}]]]]; A[n_, k_] := A[n, k] = If[n < 2, n, Sum[b[n, n + 1 - j, j, k], {j, 2, Min[n, k]}]]; T[n_, k_] := A[n, k] - If[k == 1, 0, A[n, k - 1]]; Table[Table[T[n, k], {k, 1, n}], {n, 1, 15}] // Flatten (* Jean-François Alcover, Nov 07 2017, after Alois P. Heinz *) CROSSREFS Columns k=1-10 give: A063524, A001190 (for n>1), A292229, A292230, A292231, A292232, A292233, A292234, A292235, A292236. Row sums give A000669. Limit of reversed rows gives A292087. Cf. A244372, A288942, A292085. Sequence in context: A107424 A155161 A185937 * A065177 A064044 A213980 Adjacent sequences:  A292083 A292084 A292085 * A292087 A292088 A292089 KEYWORD nonn,tabl AUTHOR Alois P. Heinz, Sep 08 2017 STATUS approved

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Last modified December 9 00:32 EST 2019. Contains 329871 sequences. (Running on oeis4.)