# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a000137 Showing 1-1 of 1 %I A000137 M1625 N0636 #31 Aug 08 2017 08:44:24 %S A000137 1,2,6,18,58,186,614,2034,6818,22970,77858,264970,905294,3102434, %T A000137 10661370,36722642,126752218,438294018,1518032598,5265341314, %U A000137 18286911130,63586988434,221342104842,771235606050,2689688538646,9388096331642 %N A000137 Series-parallel numbers. %D A000137 J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 142. %D A000137 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). %D A000137 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). %H A000137 Sean A. Irvine, Table of n, a(n) for n = 1..1000 %F A000137 G.f.: x(1+S)/(1-S), where S = g.f. for A000084. %t A000137 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-FranÃ§ois Alcover_, Feb 09 2016 *) %Y A000137 Cf. A036654, A036655, A058756, A000084. %K A000137 nonn,easy %O A000137 1,2 %A A000137 _N. J. A. Sloane_ # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE