

A050383


Permutation rooted trees with n nodes.


15



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,3


LINKS

Table of n, a(n) for n=1..26.
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)).


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] (* JeanFrançois Alcover, Oct 02 2019 *)


PROG

(PARI) {a(n)=local(A=1+x); for(i=1, n, A=1/prod(k=1, n, (1x^k*subst(A, x, x^k+x*O(x^n))))); polcoeff(A, n)} /* Paul D. Hanna */


CROSSREFS

Cf. A004111, A005355.
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



