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 A276687 Number of prime plane trees of weight prime(n). 3
 1, 1, 2, 4, 11, 30, 122, 336, 1412, 15129, 44561, 417542, 2479120, 7540843, 35983502, 451454834, 5313515136, 16809858904, 190077477328, 1124302066470, 3521811953565, 38563707677633, 240966297786218, 3192420711942298, 95433674596402663, 567734580765228356 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS A prime plane tree is either (case 1) a prime number, or (case 2) a sequence of prime plane trees whose weights are an integer partition of a prime number, where the weight of a tree is the sum of weights of its branches. Prime plane trees are "multichains" in the multiorder of integer partitions of prime numbers into prime parts (A056768). LINKS Alois P. Heinz, Table of n, a(n) for n = 1..681 Gus Wiseman, Comcategories and Multiorders, (pdf version) EXAMPLE The a(5) = 11 prime plane trees of weight A000040(5) = 11 are: {11, (3,3,5), (3,3,(2,3)), (2,2,7), (2,2,(2,5)), (2,2,(2,(2,3))), (2,2,(2,2,3)), (2,3,3,3), (2,2,2,5), (2,2,2,(2,3)), (2,2,2,2,3)}. MAPLE b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i=2, 0,        b(n, prevprime(i)))+`if`(i>n, 0, b(n-i, i)*(1+       `if`(i>2, b(i, prevprime(i)), 0))))     end: a:= n-> `if`(n<3, 1, 1+b(ithprime(n), ithprime(n-1))): seq(a(n), n=1..40);  # Alois P. Heinz, Sep 15 2016 MATHEMATICA n=20; ser=Product[1/(1-c[Prime[i]]*x^Prime[i]), {i, 1, n}]; sys=Table[c[Prime[i]]==Expand[SeriesCoefficient[ser, {x, 0, Prime[i]}]-c[Prime[i]]+1], {i, 1, n}]; Block[{c}, Set@@@sys] CROSSREFS Cf. A000040, A056768, A000607, A100118, A196545, A273873. Sequence in context: A102814 A193059 A034770 * A298891 A002387 A325922 Adjacent sequences:  A276684 A276685 A276686 * A276688 A276689 A276690 KEYWORD nonn AUTHOR Gus Wiseman, Sep 13 2016 STATUS approved

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Last modified September 27 13:48 EDT 2021. Contains 347688 sequences. (Running on oeis4.)