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 A113822 Number of binary trees of weight n where leaves have positive integer weights, where the order of subtrees is insignificant. Commutative non-associative version of partitions of n. 0
 1, 1, 2, 3, 7, 14, 35, 85, 226, 600, 1658, 4622, 13141, 37699, 109419, 320017, 943329, 2797788, 8346030, 25019401, 75340824, 227777899, 691146578, 2104028507, 6424449318, 19670277332, 60378290912, 185763773723, 572764664975 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS FORMULA a(2n) = 1 + C(a(n)+1, 2) + sum_{k=1}^{n/2-1} a(k)*a(2n-k). a(2n+1) = 1 + sum_{k=1}^{(n-1)/2} a(k)*a(2n+1-k), with a(0)=0. EXAMPLE For a(4)=7, we have the following 7 sums: 4, 3+1, 2+2, (2+1)+1, (1+1)+2, ((1+1)+1)+1, (1+1)+(1+1). CROSSREFS Cf. A007317, A000041. Sequence in context: A305785 A185089 A180564 * A036250 A191491 A210345 Adjacent sequences:  A113819 A113820 A113821 * A113823 A113824 A113825 KEYWORD easy,nonn AUTHOR Franklin T. Adams-Watters, Jan 23 2006 STATUS approved

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Last modified August 20 05:25 EDT 2019. Contains 326139 sequences. (Running on oeis4.)