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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

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..200

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 *)

CROSSREFS

Sequence in context: A231398 A231465 A208820 * A032213 A225824 A032317

Adjacent sequences:  A032298 A032299 A032300 * A032302 A032303 A032304

KEYWORD

nonn,eigen

AUTHOR

Christian G. Bower

STATUS

approved

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Last modified February 20 18:57 EST 2018. Contains 299381 sequences. (Running on oeis4.)