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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 October 24 00:04 EDT 2018. Contains 316541 sequences. (Running on oeis4.)