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 A000163 Series-parallel numbers. (Formerly M1852 N0732) 1

%I M1852 N0732

%S 2,8,34,136,538,2080,7970,30224,113874,426520,1590338,5906640,

%T 21866794,80725280,297292610,1092539736,4007553922,14675748416,

%U 53663197698,195962433328,714734393378,2603994002280,9477643739746,34463730424720

%N Series-parallel numbers.

%D J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 142.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Sean A. Irvine, <a href="/A000163/b000163.txt">Table of n, a(n) for n = 2..500</a>

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

%t 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 *)

%K nonn

%O 2,1

%A _N. J. A. Sloane_

%E More terms from _Sean A. Irvine_, Oct 14 2009

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