A007454 Number of unlabeled disconnected series-parallel posets with n nodes.

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

Author

N. J. A. Sloane, Mira Bernstein

Keywords

• nonn

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.
• Index entries for sequences related to posets

Crossrefs

Cf. A003430, A007453.

Programs

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 *)

Formula

a(n) = A003430(n) - A007453(n) for n > 1. - Sean A. Irvine, Jan 04 2018

Extensions

Name corrected by Salah Uddin Mohammad, Jun 07 2020