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A000137
Series-parallel numbers.
(Formerly M1625 N0636)
2
1, 2, 6, 18, 58, 186, 614, 2034, 6818, 22970, 77858, 264970, 905294, 3102434, 10661370, 36722642, 126752218, 438294018, 1518032598, 5265341314, 18286911130, 63586988434, 221342104842, 771235606050, 2689688538646, 9388096331642
OFFSET
1,2
REFERENCES
J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 142.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
FORMULA
G.f.: x(1+S)/(1-S), where S = g.f. for A000084.
MATHEMATICA
n = 30; s = 1/(1 - x) + O[x]^(n + 1); Do[s = s/(1 - x^k)^Coefficient[s, x^k] + O[x]^(n + 1), {k, 2, n}] ; S = s - 1; CoefficientList[(1 + S)/(1 - S) + O[x]^n, x] (* Jean-François Alcover, Feb 09 2016 *)
CROSSREFS
KEYWORD
nonn,easy
STATUS
approved