OFFSET
1,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..300
MAPLE
read transforms; A := series(exp(exp(x)-1), x, 60); A000110 := n->n!*coeff(A, x, n); [seq(A000110(i), i=1..30)]; EULERi(%);
# The function EulerInvTransform is defined in A358451.
a := EulerInvTransform(combinat:-bell):
seq(a(n), n = 1..25); # Peter Luschny, Nov 21 2022
MATHEMATICA
n=24; eq[0] = Rest[ Thread[ CoefficientList[ 1 + Series[ Sum[ BellB[k]*x^k, {k, 1, n}] - Product[1/(1-x^k)^a[k], {k, 1, n}], {x, 0, n}], x] == 0]]; s[1] = First[ Solve[ First[eq[0]], a[1]]]; Do[eq[k] = Rest[eq[k-1]] /. s[k]; s[k+1] = First[ Solve[ First[eq[k]], a[k+1]]], {k, 1, n-1}]; Table[a[k], {k, 1, n}] /. Flatten[Table[s[k], {k, 1, n}]] (* Jean-François Alcover, Jul 26 2011 *)
bb = Array[BellB, n = 25]; s = {}; For[i = 1, i <= n, i++, AppendTo[s, i* bb[[i]] - Sum[s[[d]]*bb[[i-d]], {d, i-1}]]]; Table[Sum[If[Divisible[i, d], MoebiusMu[i/d], 0]*s[[d]], {d, 1, i}]/i, {i, n}] (* Jean-François Alcover, Apr 15 2016 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jul 18 2003
STATUS
approved