A000137 Series-parallel numbers.
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
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
- Sean A. Irvine, Table of n, a(n) for n = 1..1000
Programs
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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 *)
Formula
G.f.: x(1+S)/(1-S), where S = g.f. for A000084.