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 A292085 Number A(n,k) of (unlabeled) rooted trees with n leaf nodes and without unary nodes or outdegrees larger than k; square array A(n,k), n>=0, k>=0, read by antidiagonals. 12
 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 2, 2, 0, 1, 1, 2, 4, 3, 0, 1, 1, 2, 5, 9, 6, 0, 1, 1, 2, 5, 11, 23, 11, 0, 1, 1, 2, 5, 12, 30, 58, 23, 0, 1, 1, 2, 5, 12, 32, 80, 156, 46, 0, 1, 1, 2, 5, 12, 33, 87, 228, 426, 98, 0, 1, 1, 2, 5, 12, 33, 89, 251, 656, 1194, 207, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,13 LINKS Alois P. Heinz, Antidiagonals n = 1..141, flattened FORMULA A(n,k) = Sum_{j=1..k} A292086(n,j). EXAMPLE :               T(4,3) = 4             : :                                      : :       o       o         o       o    : :      / \     / \       / \     /|\   : :     o   N   o   o     o   N   o N N  : :    / \     ( ) ( )   /|\     ( )     : :   o   N    N N N N  N N N    N N     : :  ( )                                 : :  N N                                 : :                                      : Square array A(n,k) begins:   1,  1,   1,   1,   1,   1,   1,   1, ...   0,  1,   1,   1,   1,   1,   1,   1, ...   0,  1,   2,   2,   2,   2,   2,   2, ...   0,  2,   4,   5,   5,   5,   5,   5, ...   0,  3,   9,  11,  12,  12,  12,  12, ...   0,  6,  23,  30,  32,  33,  33,  33, ...   0, 11,  58,  80,  87,  89,  90,  90, ...   0, 23, 156, 228, 251, 258, 260, 261, ... 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

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Last modified January 20 19:43 EST 2019. Contains 319335 sequences. (Running on oeis4.)