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 A301706 Number of rooted thrice-partitions of n. 16
 1, 1, 2, 4, 9, 19, 43, 91, 201, 422, 918, 1896, 4089, 8376, 17793, 36445, 76446, 155209, 324481, 655426, 1355220, 2741092, 5617505, 11291037, 23086423, 46227338, 93753196, 187754647, 378675055, 754695631, 1518414812, 3016719277, 6037006608, 11984729983 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS A rooted partition of n is an integer partition of n - 1. A rooted twice-partition of n is a choice of a rooted partition of each part in a rooted partition of n. A rooted thrice-partition of n is a choice of a rooted twice-partition of each part in a rooted partition of n. LINKS EXAMPLE The a(5) = 9 rooted thrice-partitions: ((2)), ((11)), ((1)()), (()()()), ((1))(), (()())(), (())(()), (())()(), ()()()(). The a(6) = 19 rooted thrice-partitions: ((3)), ((21)), ((111)), ((2)()), ((11)()), ((1)(1)), ((1)()()), (()()()()), ((2))(), ((11))(), ((1)())(), (()()())(), ((1))(()), (()())(()), ((1))()(), (()())()(), (())(())(), (())()()(), ()()()()(). MATHEMATICA twire[n_]:=twire[n]=Sum[Times@@PartitionsP/@(ptn-1), {ptn, IntegerPartitions[n-1]}]; thrire[n_]:=Sum[Times@@twire/@ptn, {ptn, IntegerPartitions[n-1]}]; Array[thrire, 30] CROSSREFS Cf. A000041, A001383, A002865, A063834, A093637, A119442, A196545, A281113, A289501, A300383, A301422, A301462, A301467, A301480,  A301595, A301598. Sequence in context: A192673 A193021 A112569 * A289845 A101463 A319379 Adjacent sequences:  A301703 A301704 A301705 * A301707 A301708 A301709 KEYWORD nonn AUTHOR Gus Wiseman, Mar 25 2018 STATUS approved

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Last modified May 31 00:29 EDT 2020. Contains 334747 sequences. (Running on oeis4.)