A058475 Total number of interior nodes in all series-parallel networks with n labeled edges, multiple edges not allowed.

0, 0, 1, 5, 41, 394, 4704, 65386, 1049754, 19032392, 385419072, 8615947592, 210831826952, 5604404196832, 160834760288864, 4955867959526784, 163197046787269792, 5719576163352685696, 212565832527352216928, 8350117027586731306848

Offset

0,4

References

J. W. Moon, Some enumerative results on series-parallel networks, Annals Discrete Math., 33 (1987), 199-226 (the sequence I_V(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); CoefficientList[ Series[ev, {x, 0, max}], x]*Range[0, max]! (* Jean-François Alcover, Feb 01 2013 *)

Crossrefs

Sequence in context: A083884 A156153 A026000 * A199684 A177506 A064087

Adjacent sequences: A058472 A058473 A058474 * A058476 A058477 A058478

Keyword

nonn,nice,easy

Author

N. J. A. Sloane, Dec 20 2000

Status

approved