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 A244925 Number T(n,k) of n-node unlabeled rooted trees with every leaf at height k; triangle T(n,k), n>=1, 0<=k<=n-1, read by rows. 19
 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 2, 1, 1, 0, 1, 2, 2, 1, 1, 0, 1, 4, 3, 2, 1, 1, 0, 1, 4, 5, 3, 2, 1, 1, 0, 1, 7, 7, 6, 3, 2, 1, 1, 0, 1, 8, 12, 8, 6, 3, 2, 1, 1, 0, 1, 12, 18, 15, 9, 6, 3, 2, 1, 1, 0, 1, 14, 27, 23, 16, 9, 6, 3, 2, 1, 1, 0, 1, 21, 42, 39, 26, 17, 9, 6, 3, 2, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,13 LINKS Alois P. Heinz, Rows n = 1..141, flattened EXAMPLE The A048816(5) = 5 rooted trees with 5 nodes with every leaf at the same height sorted by height are:   :    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  :   :         :             :       :     :   : ---1--- : -----2----- : --3-- : -4- : Thus row 5 = [0, 1, 2, 1, 1]. Triangle T(n,k) begins:   1;   0, 1;   0, 1,  1;   0, 1,  1,  1;   0, 1,  2,  1,  1;   0, 1,  2,  2,  1,  1;   0, 1,  4,  3,  2,  1, 1;   0, 1,  4,  5,  3,  2, 1, 1;   0, 1,  7,  7,  6,  3, 2, 1, 1;   0, 1,  8, 12,  8,  6, 3, 2, 1, 1;   0, 1, 12, 18, 15,  9, 6, 3, 2, 1, 1;   0, 1, 14, 27, 23, 16, 9, 6, 3, 2, 1, 1;   ... MAPLE with(numtheory): T:= proc(n, k) option remember; `if`(n=1, 1, `if`(k=0, 0,       add(add(`if`(d0), A002865(n-1) (for n>2), A048808, A048809, A048810, A048811, A048812, A048813, A048814, A048815. T(2n+1,n) gives A074045. Row sums give A048816. Sequence in context: A072233 A264391 A116598 * A068914 A090824 A264620 Adjacent sequences:  A244922 A244923 A244924 * A244926 A244927 A244928 KEYWORD nonn,tabl AUTHOR Alois P. Heinz, Jul 08 2014 STATUS approved

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Last modified July 29 04:15 EDT 2021. Contains 346340 sequences. (Running on oeis4.)