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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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified August 13 16:51 EDT 2024. Contains 375144 sequences. (Running on oeis4.)