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 A032301 Shifts left under "EFJ" (unordered, size, labeled) transform. 2
 1, 1, 1, 4, 8, 38, 206, 1200, 6824, 50912, 446752, 3828592, 38953680, 411358960, 4740541440, 57933236928, 759535226432, 10488778719488, 156933187370432, 2425018017191040, 40031753222399360, 689218695990369536, 12461424512466701312, 234386152841716303616 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS a(n) is the number of increasing rooted trees where any 2 subtrees extending from the same node have a different number of nodes (the unlabeled trees counted by A032305). An increasing tree is labeled so that every path from the root to an external node is increasing. - Geoffrey Critzer, Jul 29 2013 (a(n)/n!)^(1/n) tends to 0.82143368... - Vaclav Kotesovec, Jul 21 2019 LINKS Alois P. Heinz, Table of n, a(n) for n = 1..200 Vaclav Kotesovec, Plot of a(n+1)/a(n)/n for n = 1..3300 FORMULA E.g.f.: A(x) satisfies: A'(x) = Product_{n>=1} 1 + a(n) x^n/n!. - Geoffrey Critzer, Jul 29 2013 MAPLE with(combinat): b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,       add(multinomial(n, i\$j, n-i*j)*binomial(b((i-1)\$2), j)        *b(n-i*j, i-1), j=0..min(1, n/i))))     end: a:= n-> b((n-1)\$2): seq(a(n), n=1..30);  # Alois P. Heinz, Jul 31 2013 MATHEMATICA nn=15; f[x_]:=Sum[a[n]x^n/n!, {n, 0, nn}]; sol=SolveAlways[0==Series[f[x] -Integrate[Product[1+a[i]x^i/i!, {i, 1, nn}], x], {x, 0, nn}], x]; Table[a[n], {n, 0, nn}]/.sol (* Geoffrey Critzer, Jul 29 2013 *) PROG (PARI) EFJ(v)={Vec(serlaplace(prod(k=1, #v, 1 + v[k]*x^k/k! + O(x*x^#v)))-1, -#v)} seq(n)={my(v=[1]); for(n=2, n, v=concat([1], EFJ(v))); v} \\ Andrew Howroyd, Sep 11 2018 CROSSREFS Sequence in context: A231398 A231465 A208820 * A032213 A225824 A032317 Adjacent sequences:  A032298 A032299 A032300 * A032302 A032303 A032304 KEYWORD nonn,eigen AUTHOR STATUS approved

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Last modified August 16 12:15 EDT 2022. Contains 356168 sequences. (Running on oeis4.)