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A007454
Number of unlabeled disconnected series-parallel posets with n nodes.
(Formerly M1630)
5
1, 1, 2, 6, 18, 64, 227, 856, 3280, 12885, 51342, 207544, 847886, 3497384, 14541132, 60884173, 256480895, 1086310549, 4623128656, 19759964149, 84784735379, 365066645854, 1576927900803, 6831518134251, 29674505668536, 129216630647787, 563949605921815
OFFSET
1,3
COMMENTS
a(1) = 0 would make more sense, but original article has a(1) = 1. - Sean A. Irvine, Jan 04 2018
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..1000 (first 100 terms from Jean-François Alcover)
P. J. Cameron, Some sequences of integers, Discrete Math., 75 (1989), 89-102.
P. J. Cameron, Some sequences of integers, in "Graph Theory and Combinatorics 1988", ed. B. Bollobas, Annals of Discrete Math., 43 (1989), 89-102.
FORMULA
a(n) = A003430(n) - A007453(n) for n > 1. - Sean A. Irvine, Jan 04 2018
MATHEMATICA
terms = 25; A[_] = 1;
Do[A[x_] = Exp[Sum[(1/k)*(A[x^k] + 1/A[x^k] - 2 + x^k), {k, 1, terms + 1}]] + O[x]^(terms + 1) // Normal, terms + 1];
A003430 = CoefficientList[A[x], x] // Rest;
mob[m_, n_] := If[Mod[m, n] == 0, MoebiusMu[m/n], 0];
EULERi[b_] := Module[{a, c, i, d}, c = {}; For[i = 1, i <= Length[b], i++, c = Append[c, i*b[[i]] - Sum[c[[d]]*b[[i - d]], {d, 1, i - 1}]]]; a = {}; For[i = 1, i <= Length[b], i++, a = Append[a, (1/i)*Sum[mob[i, d]*c[[d]], {d, 1, i}]]]; Return[a]];
Join[{1}, Rest[A003430 - EULERi[A003430]]] (* Jean-François Alcover, Jan 23 2020 *)
CROSSREFS
Sequence in context: A150070 A150071 A265945 * A305578 A150072 A150073
KEYWORD
nonn
EXTENSIONS
Name corrected by Salah Uddin Mohammad, Jun 07 2020
STATUS
approved