OFFSET
0,3
COMMENTS
A free pure symmetric multifunction (with empty expressions allowed) f in EOME is either (case 1) a positive integer, or (case 2) a possibly empty expression of the form h[g_1, ..., g_k] where k >= 0, h is in EOME, each of the g_i for i = 1, ..., k is in EOME, and for i < j we have g_i <= g_j under a canonical total ordering of EOME, such as the Mathematica ordering of expressions.
Also the number of inequivalent colorings of orderless Mathematica expressions with n positions.
EXAMPLE
Inequivalent representatives of the a(3) = 11 colorings:
1[1,1] 1[2,2] 1[1,2] 1[2,3]
1[1[]] 1[2[]]
1[][1] 1[][2]
1[1][] 1[2][]
1[][][]
PROG
(PARI) \\ See links in A339645 for combinatorial species functions.
cycleIndexSeries(n)={my(p=O(x)); for(n=1, n, p = x*sv(1) + x*p*sExp(p)); p}
InequivalentColoringsSeq(cycleIndexSeries(15)) \\ Andrew Howroyd, Dec 30 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 17 2018
EXTENSIONS
Terms a(8) and beyond from Andrew Howroyd, Dec 30 2020
STATUS
approved