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A003084 Related to number of digraphs.
(Formerly M3993)
2
1, 5, 40, 801, 46821, 9185102, 6163297995, 14339791643249, 117235455142196308, 3412474003994007703605, 357748249084029269153547905, 136400554886800212073525651823742 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 124, table 5.1.2, p*a_p

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Table of n, a(n) for n=1..12.

FORMULA

Sum a(n) x^n / n = log (1 + Sum d(n) x^n ), where d(n) is # digraphs on n nodes (A000273 ).

MATHEMATICA

Needs["Combinatorica`"]; d[n_] := GraphPolynomial[n, x, Directed] /. x -> 1; max = 12; se = Series[ Sum[ a[n]*x^n/n, {n, 1, max}] - Log[1 + Sum[ d[n]*x^n, {n, 1, max}]], {x, 0, max}]; sol = SolveAlways[ se == 0, x]; A003084 = Table[ a[n], {n, 1, max}] /. sol[[1]] (* Jean-Fran├žois Alcover, Feb 01 2012, after formula *)

CROSSREFS

Sequence in context: A280572 A217904 A005330 * A010573 A043083 A041599

Adjacent sequences:  A003081 A003082 A003083 * A003085 A003086 A003087

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Corrected and extended by Vladeta Jovovic, Jan 09 2000

STATUS

approved

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Last modified November 14 17:12 EST 2018. Contains 317210 sequences. (Running on oeis4.)