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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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

Crossrefs

Cf. A036654, A036655, A058756, A000084.

Programs

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.