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 A032009 Number of planted planar trees (n+1 nodes) where any 2 subtrees extending from the same node have a different number of nodes. 3
 1, 1, 1, 3, 5, 13, 35, 95, 249, 691, 2007, 5719, 16823, 49371, 146755, 438301, 1319343, 3981699, 12129477, 36987253, 113456615, 348921105, 1077206189, 3332120237, 10347481901, 32183230157, 100372658801, 313633257399, 982232930081, 3080379360481, 9681909324247 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Number of compositions of n-1 into distinct parts if there are a(i) kinds of part i. a(6) = 13: 5, 5', 5'', 5''', 5'''', 41, 4'1, 4''1, 14, 14', 14'', 32, 23. LINKS Alois P. Heinz, Table of n, a(n) for n = 1..1938 FORMULA Shifts left under "AFK" (ordered, size, unlabeled) transform MAPLE b:= proc(n, i, p) option remember; `if`(n=0, p!, `if`(i<1, 0,       b(n, i-1, p) +`if`(i>n, 0, a(i)*b(n-i, i-1, p+1))))     end: a:= n-> b(n-1\$2, 0): seq(a(n), n=1..40);  # Alois P. Heinz, Sep 05 2015 MATHEMATICA b[n_, i_, p_] := b[n, i, p] = If[n==0, p!, If[i<1, 0, b[n, i-1, p] + If[ i>n, 0, a[i]*b[n-i, i-1, p+1]]]]; a[n_] := b[n-1, n-1, 0]; Table[a[n], {n, 1, 40}] (* Jean-François Alcover, Feb 24 2016, after Alois P. Heinz *) PROG (PARI) AFK(v)={apply(p->subst(serlaplace(y^0*p), y, 1), Vec(prod(k=1, #v, 1 + v[k]*x^k*y + O(x*x^#v))))} seq(n)={my(v=[1]); for(i=1, n, v=AFK(v)); v} \\ Andrew Howroyd, Jun 21 2018 CROSSREFS Cf. A261894. Sequence in context: A296023 A027039 A283844 * A032027 A005383 A175257 Adjacent sequences:  A032006 A032007 A032008 * A032010 A032011 A032012 KEYWORD nonn,eigen AUTHOR EXTENSIONS More terms from Alois P. Heinz, Sep 05 2015 STATUS approved

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Last modified October 21 10:29 EDT 2018. Contains 316414 sequences. (Running on oeis4.)