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A058388 Total number of interior nodes in all essentially parallel series-parallel networks with n labeled edges, multiple edges not allowed. 3
0, 0, 0, 3, 14, 195, 2059, 31150, 489012, 9073638, 183490118, 4135560660, 101421574440, 2706766547628, 77860733488732, 2405136817507216, 79353915366944784, 2786110796782734528, 103703080088989729280, 4079350129335095498048 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Feb 01 2013 *)

CROSSREFS

Sequence in context: A250001 A288559 A132490 * A327230 A288555 A288563

Adjacent sequences:  A058385 A058386 A058387 * A058389 A058390 A058391

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane, Dec 20 2000

STATUS

approved

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Last modified December 9 09:33 EST 2019. Contains 329877 sequences. (Running on oeis4.)