A000163 Series-parallel numbers.

2, 8, 34, 136, 538, 2080, 7970, 30224, 113874, 426520, 1590338, 5906640, 21866794, 80725280, 297292610, 1092539736, 4007553922, 14675748416, 53663197698, 195962433328, 714734393378, 2603994002280, 9477643739746, 34463730424720

Offset: 2

Author

N. J. A. Sloane

Keywords

• nonn

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 = 2..500

Programs

Mathematica

n = 25; 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[2*(1 + S)/(1 - S)^3 + O[x]^n, x] (* Jean-François Alcover, Feb 09 2016 *)

Formula

G.f.: 2*(1+S)/(1-S)^3, where S = g.f. for A000084. [Sean A. Irvine, Oct 14 2009]

Extensions

More terms from Sean A. Irvine, Oct 14 2009