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 A301462 Number of enriched r-trees of size n. 27
 1, 2, 3, 8, 23, 77, 254, 921, 3249, 12133, 44937, 172329, 654895, 2565963, 9956885, 39536964, 156047622, 626262315, 2499486155, 10129445626, 40810378668, 166475139700, 676304156461, 2775117950448, 11342074888693, 46785595997544, 192244951610575, 796245213910406 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS An enriched r-tree of size n > 0 is either a single node of size n, or a finite sequence of enriched r-trees with weakly decreasing sizes summing to n - 1. These are different from the R-trees of data science and the enriched R-trees of Bousquet-MÃ©lou and Courtiel. LINKS Andrew Howroyd, Table of n, a(n) for n = 0..500 FORMULA O.g.f.: 1/(1 - x) + x Product_{i > 0} 1/(1 - a(i) x^i). EXAMPLE The a(3) = 8 enriched r-trees: 3, (2), ((1)), ((())), (11), (1()), (()1), (()()). MATHEMATICA ert[n_]:=ert[n]=1+Sum[Times@@ert/@y, {y, IntegerPartitions[n-1]}]; Array[ert, 30] PROG (PARI) seq(n)={my(v=vector(n)); for(n=1, n, v[n] = 1 + polcoef(1/prod(k=1, n-1, 1 - v[k]*x^k + O(x^n)), n-1)); concat([1], v)} \\ Andrew Howroyd, Aug 26 2018 CROSSREFS Cf. A000081, A003238, A004111, A032305, A055277, A093637, A127524, A196545, A289501, A290689, A300443, A301342-A301345, A301364-A301368, A301422, A301467, A301469, A301470. Sequence in context: A261061 A086628 A032096 * A120763 A120708 A327009 Adjacent sequences:  A301459 A301460 A301461 * A301463 A301464 A301465 KEYWORD nonn AUTHOR Gus Wiseman, Mar 21 2018 STATUS approved

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Last modified May 22 20:00 EDT 2022. Contains 353957 sequences. (Running on oeis4.)