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

1,3

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

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

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 *)

Prog

(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 */

Crossrefs

Cf. A004111, A005355, A091865, A308368.

Sequence in context: A148791 A148792 A007563 * A060404 A192905 A192207

Adjacent sequences: A050380 A050381 A050382 * A050384 A050385 A050386

Keyword

nonn,eigen

Author

Christian G. Bower, Nov 15 1999

Status

approved