A058388 Total number of interior nodes in all essentially parallel series-parallel networks with n labeled edges, multiple edges not allowed.

0, 0, 0, 3, 14, 195, 2059, 31150, 489012, 9073638, 183490118, 4135560660, 101421574440, 2706766547628, 77860733488732, 2405136817507216, 79353915366944784, 2786110796782734528, 103703080088989729280, 4079350129335095498048

Offset

0,4

References

J. W. Moon, Some enumerative results on series-parallel networks, Annals Discrete Math., 33 (1987), 199-226 (the sequence I_Q(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); eq = (ev + v)/(1 + v) - q; CoefficientList[ Series[eq, {x, 0, max}], x]*Range[0, max]! (* Jean-François Alcover, Feb 01 2013 *)

Crossrefs

Sequence in context: A366715 A132490 A344745 * A362385 A327230 A288555

Adjacent sequences: A058385 A058386 A058387 * A058389 A058390 A058391

Keyword

nonn,easy,nice

Author

N. J. A. Sloane, Dec 20 2000

Status

approved