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 A317883 Number of free pure achiral multifunctions with one atom and n positions. 6
 1, 0, 1, 1, 3, 4, 10, 17, 37, 70, 150, 299, 634, 1311, 2786, 5879, 12584, 26904, 58005, 125242, 271819, 591297, 1290976, 2825170, 6199964, 13635749, 30057649, 66386206, 146903289, 325637240, 723024160, 1607805207, 3580476340, 7984266625, 17827226469 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS A free pure achiral multifunction (PAM) is either (case 1) the leaf symbol "o", or (case 2) a nonempty expression of the form h[g, ..., g] where h and g are PAMs. The number of positions in a PAM is the number of brackets [...] plus the number of o's. LINKS Andrew Howroyd, Table of n, a(n) for n = 1..200 FORMULA a(1) = 1; a(n > 1) = Sum_{0 < k < n - 1} a(k) * Sum_{d|(n - k - 1)} a(d). G.f. A(x) satisfies: A(x) = x * (1 + A(x) * Sum_{k>=1} A(x^k)). - Ilya Gutkovskiy, May 03 2019 EXAMPLE The a(7) = 10 PAMs: o[o[o[o]]] o[o[o][o]] o[o][o[o]] o[o[o]][o] o[o][o][o] o[o[o,o,o]] o[o][o,o,o] o[o,o][o,o] o[o,o,o][o] o[o,o,o,o,o] MATHEMATICA a[n_]:=If[n==1, 1, Sum[a[k]*Sum[a[d], {d, Divisors[n-k-1]}], {k, n-2}]]; Array[a, 12] PROG (PARI) seq(n)={my(p=O(x)); for(n=1, n, p = x + p*x*sum(k=1, n-2, subst(p + O(x^(n\k+1)), x, x^k) ) + O(x*x^n)); Vec(p)} \\ Andrew Howroyd, Aug 19 2018 (PARI) seq(n)={my(v=vector(n)); v[1]=1; for(n=2, #v, v[n]=sum(i=1, n-2, v[i]*sumdiv(n-i-1, d, v[d]))); v} \\ Andrew Howroyd, Aug 19 2018 CROSSREFS Cf. A002033, A003238, A052893, A053492, A214577, A277996, A280000, A317853, A317875. Cf. A317882, A317884, A317885. Sequence in context: A034774 A342536 A172416 * A337089 A144958 A034775 Adjacent sequences: A317880 A317881 A317882 * A317884 A317885 A317886 KEYWORD nonn AUTHOR Gus Wiseman, Aug 09 2018 EXTENSIONS Terms a(13) and beyond from Andrew Howroyd, Aug 19 2018 STATUS approved

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Last modified September 23 13:57 EDT 2023. Contains 365551 sequences. (Running on oeis4.)