A000527 Series-parallel numbers. (Formerly M5304 N2306)

52, 472, 3224, 18888, 101340, 511120, 2465904, 11496144, 52165892, 231557064, 1009247192, 4331502840, 18346242492, 76822836544, 318485778848, 1308750158016, 5335993098340, 21603437175288, 86912657626392, 347660876627944, 1383457374046444, 5479086968052912, 21604984733546336, 84850331177724944, 332001521469767940, 1294589169323791912, 5031934808360234760, 19500424806065865400, 75360646947991208396, 290478417300879735680, 1116919455364101145920, 4284817000807140094464, 16402243457215852326116, 62659647762404302956856, 238910441445219175239480

Offset

4,1

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

Table of n, a(n) for n=4..38.

Formula

G.f.: 4(13+14S+3S^2)(1+S)/(1-S)^7, where S = g.f. for A000084. - Sean A. Irvine, Nov 14 2010

Mathematica

n = 35; 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[4 (13 + 14 S + 3 S^2) (1 + S)/(1 - S)^7 + O[x]^n, x] (* Jean-François Alcover, Feb 09 2016 *)

Crossrefs

Sequence in context: A257940 A005946 A200549 * A294055 A285753 A100413

Adjacent sequences: A000524 A000525 A000526 * A000528 A000529 A000530

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Sean A. Irvine, Nov 14 2010

Status

approved