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A007649
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Number of set-like molecular species of degree n.
(Formerly M0824)
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2
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1, 1, 2, 3, 7, 9, 20, 26, 54, 74, 137, 184, 356, 473, 841, 1154, 2034, 2742, 4740, 6405, 10874, 14794, 24515, 33246, 54955, 74380, 120501, 163828, 263144, 356621, 567330, 768854, 1212354, 1644335, 2567636, 3478873, 5403223, 7314662, 11265825, 15258443, 23363143, 31608055, 48113280, 65063640, 98501538, 133168305, 200503864
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OFFSET
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0,3
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COMMENTS
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A set-like molecular species is formed from the species of sets, E, through species addition, product and substitution.
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REFERENCES
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G. Labelle and P. Leroux, Identities and enumeration: weighting connected components, Abstracts Amer. Math. Soc., 15 (1994), Meeting #896.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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MATHEMATICA
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NN = 66; va = Array[0&, NN]; va[[1]] = 0; va[[2]] = 1; vm = Array[0&, NN]; vm[[1]] = 1; vm[[2]] = 1; For[n = 2, n <= NN - 1, n++, va[[n+1]] = DivisorSum[n , vm[[#+1]]&]; vm[[n+1]] = 1/n*Sum[DivisorSum[k, #*va[[#+1]] &]*vm[[n-k+1]], {k, 1, n}]]; vm (* Jean-François Alcover, Dec 01 2015, adapted from Joerg Arndt's PARI script *)
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PROG
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(PARI) /* From the Labelle/Leroux reference */
N=66; /* that many terms */
va=vector(N); va[0+1] = 0; va[1+1] = 1;
vm=vector(N); vm[0+1] = 1; vm[1+1] = 1;
{ for(n=2, N-1,
va[n+1] = sumdiv(n, k, vm[k+1]);
vm[n+1] = 1/n * sum(k=1, n, sumdiv(k, d, d*va[d+1]) * vm[n-k+1] );
); }
v007649=vm
/* v007650=va */
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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