A228160 Number of sets (forests) of labeled identity trees (trees enumerated by A228159) with n nodes.

1, 1, 3, 13, 97, 861, 10171, 144313, 2425473, 46361017, 1008845011, 24440301381, 653993215393, 19126571703253, 607566772915467, 20816075734498801, 765497764431847681, 30064774690536609393, 1256227494273614356003, 55637289075570248646397, 2603702479493046357670881

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..150

Formula

E.g.f.: exp(A(x)) where A(x) is the e.g.f. for A228159.

Maple

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
      add(binomial(b(i-1$2), j)*b(n-i*j, i-1), j=0..n/i)))
    end:
a:= proc(n) option remember; `if`(n=0, 1,
      add(binomial(n-1, j-1) *j!*b(j-1$2)*a(n-j), j=1..n))
    end:
seq(a(n), n=0..25);  # Alois P. Heinz, Aug 14 2013

Mathematica

nn = 20; SolveAlways[
0 == Series[
   f[x] - x Product[(1 + x^i)^(a[i]/i!), {i, 1, nn}], {x, 0,
    nn}], x]; b = Sum[a[n] x^n/n!, {n, 1, nn}] /. sol;
Range[0, nn]! Flatten[CoefficientList[Series[Exp[b], {x, 0, nn}], x]]

Crossrefs

Sequence in context: A275528 A129375 A293528 * A371319 A085023 A144276

Adjacent sequences: A228157 A228158 A228159 * A228161 A228162 A228163

Keyword

nonn

Author

Geoffrey Critzer, Aug 14 2013

Status

approved