A058406 - OEIS

A058406

Total number of interior nodes in all series-parallel networks with n labeled edges, multiple edges not allowed.

0, 0, 1, 2, 27, 199, 2645, 34236, 560742, 9958754, 201928954, 4480386932, 109410252512, 2897637649204, 82974026800132, 2550731142019568, 83843131420325008, 2933465366569951168, 108862752438362487648, 4270766898251635808800

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OFFSET

0,4

REFERENCES

J. W. Moon, Some enumerative results on series-parallel networks, Annals Discrete Math., 33 (1987), 199-226 (the sequence I_R(n)*Q_pi).

LINKS

Table of n, a(n) for n=0..19.

Index entries for sequences mentioned in Moon (1987)

FORMULA

Let Q, R = Q-log(1+x), V=Q+R be the e.g.f.'s for A058379, A058380, A058381 resp. E.g.f.'s for A058475, A058406, A058388 are E_V = (V*Q-R)/(1-V), E_R = E_V/(1+V), E_Q = (E_V+V)/(1+V)-Q.

MATHEMATICA

max = 19; q = CoefficientList[ InverseSeries[ Series[-1 + E^(1 + 2*a - E^a), {a, 0, max}], x], x]*Table[x^k, {k, 0, max}] // Total; r = q - Log[1 + x]; v = q + r; ev = (v*q - r)/(1 - v); er = ev/(1 + v); CoefficientList[ Series[er, {x, 0, max}], x]*Range[0, max]! (* Jean-François Alcover, Feb 01 2013 *)

CROSSREFS

Sequence in context: A098627 A263930 A051766 * A216087 A049070 A197316

Adjacent sequences: A058403 A058404 A058405 * A058407 A058408 A058409

KEYWORD

nonn,nice,easy

AUTHOR

N. J. A. Sloane, Dec 20 2000

STATUS

approved