A000163 Series-parallel numbers. (Formerly M1852 N0732)

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

2,1

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 = 2..500

Formula

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

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 *)

Crossrefs

Sequence in context: A204090 A226495 A111643 * A117616 A345757 A369836

Adjacent sequences: A000160 A000161 A000162 * A000164 A000165 A000166

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Sean A. Irvine, Oct 14 2009

Status

approved