OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1717
Håvard Berland, Brynjulf Owren and Bård Skaflestad, B-series and order conditions for exponential integrators, 2004. See p. 6.
F. Chapoton, F. Hivert, and J.-C. Novelli, A set-operad of formal fractions and dendriform-like sub-operads, arXiv preprint arXiv:1307.0092 [math.CO], 2013.
F. Chapoton, F. Hivert, and J.-C. Novelli, A set-operad of formal fractions and dendriform-like sub-operads, Journal of Algebra, 465 (2016), 322-355.
Timothy Y. Chow and Mark G. Tiefenbruck, The Latin Tableau Conjecture, 2024. See p. 11.
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 768
FORMULA
G.f. satisfies: A(x) = x*exp( Sum_{n>=1} (A(x^n) + x^n)/n ). - Paul D. Hanna, Oct 19 2005
If b(n) is the Euler transform of a(n), A052855, then a(n+1) = a(n) + b(n). - Franklin T. Adams-Watters, Mar 09 2006
G.f.: (x/(1 - x)) * Product_{n>=1} 1/(1 - x^n)^a(n). - Ilya Gutkovskiy, Jun 28 2021
MAPLE
b:= proc(n) option remember; `if`(n=0, 1, add(b(n-j)*
add(d*a(d), d=numtheory[divisors](j)), j=1..n)/n)
end:
a:= proc(n) option remember; `if`(n=0, 0, a(n-1)+b(n-1)) end:
seq(a(n), n=0..35); # Alois P. Heinz, Jun 13 2018
MATHEMATICA
max = 27; A[_] = 1; Do[A[x_] = x*Exp[Sum[(A[x^k] + x^k)/k + O[x]^n, {k, 1, n}]] // Normal, {n, 1, max}]; CoefficientList[A[x] + O[x]^max, x] (* Jean-François Alcover, May 25 2018 *)
PROG
(PARI) {a(n)=local(A=x+x*O(x^n)); for(i=1, n, A=x*exp(sum(m=1, n, (subst(A, x, x^m)+x^m)/m))); polcoeff(A, n, x)} \\ Paul D. Hanna, Oct 19 2005
CROSSREFS
KEYWORD
nonn,changed
AUTHOR
Christian G. Bower, Nov 15 1998
STATUS
approved