A050383 Permutation rooted trees with n nodes.
1, 1, 3, 8, 25, 77, 262, 897, 3208, 11658, 43243, 162477, 618219, 2374699, 9200541, 35903017, 140997527, 556798525, 2209685939, 8807924914, 35248187347, 141564134395, 570402287162, 2305138038036, 9340981510156, 37946616550787
Offset: 1
Links
- Vaclav Kotesovec, Table of n, a(n) for n = 1..240
- C. G. Bower, Transforms (2)
- INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 773
- N. J. A. Sloane, Transforms
- Index entries for sequences related to rooted trees
Programs
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Mathematica
m = 26; A[_] = 0; Do[A[x_] = 1/Product[1 - x^n A[x^n], {n, 1, m}] + O[x]^m // Normal, {m}]; CoefficientList[A[x], x] (* Jean-François Alcover, Oct 02 2019 *) -
PARI
{a(n)=local(A=1+x); for(i=1, n, A=1/prod(k=1, n, (1-x^k*subst(A,x,x^k+x*O(x^n))))); polcoeff(A, n)} /* Paul D. Hanna */
Formula
G.f. (with offset 0) satisfies: A(x) = 1/Product_{n>=1} (1 - x^n*A(x^n)). - Paul D. Hanna, Sep 28 2011
Shifts left under transform T where Ta is EULER(CIK(a)).
a(n) ~ c * d^n / n^(3/2), where d = 4.313133937842504228... and c = 0.153549235191409889... - Vaclav Kotesovec, Nov 05 2021