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

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