A007454 Number of unlabeled disconnected series-parallel posets with n nodes. (Formerly M1630)

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.

Index entries for sequences related to posets

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

Cf. A003430, A007453.

Sequence in context: A150070 A150071 A265945 * A305578 A150072 A150073

Adjacent sequences: A007451 A007452 A007453 * A007455 A007456 A007457

Keyword

nonn

Author

N. J. A. Sloane, Mira Bernstein

Extensions

Name corrected by Salah Uddin Mohammad, Jun 07 2020

Status

approved