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A028418
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Sum over all n! permutations of n letters of maximum cycle length.
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7
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1, 3, 13, 67, 411, 2911, 23563, 213543, 2149927, 23759791, 286370151, 3734929903, 52455166063, 788704078527, 12648867695311, 215433088624351, 3884791172487903, 73919882720901823, 1480542628345939807
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967, p. 183.
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LINKS
| Ph. Flajolet and A. Odlyzko, Singularity analysis of generating functions, p. 22.
Thomas Dybdahl Ahle, Table of n, a(n) for n = 1..142
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FORMULA
| E.g.f.: sum(k>=0, 1/(1-x) - exp(sum(j=1..k, x^j/j )) ).
a(n) = f(n,0,n,n!) where f(l,r,n,m) = m*r if r >= l, otherwise sum(f(k,max(l-k,r),n-1,m/n) for k=0 to l-1) + (n-l)*f(l,r,n-1,m/n). [Thomas Dybdahl Ahle, Aug 15 2011]
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MATHEMATICA
| kmax = 19; gf[x_] = Sum[ 1/(1-x) - 1/(E^((x^(1+k)*Hypergeometric2F1[1+k, 1, 2+k, x])/ (1+k))*(1-x)), {k, 0, kmax}];
a[n_] := n!*Coefficient[Series[gf[x], {x, 0, kmax}], x^n]; Array[a, kmax]
(* From Jean-François Alcover, Jun 22 2011, after e.g.f. *)
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CROSSREFS
| Cf. A060014, A006128, A028417.
Sequence in context: A064062 A114191 A107592 * A180191 A080832 A194019
Adjacent sequences: A028415 A028416 A028417 * A028419 A028420 A028421
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KEYWORD
| nonn
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AUTHOR
| Joe Keane (jgk(AT)jgk.org)
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EXTENSIONS
| More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 19 2002
More terms from Thomas Dybdahl Ahle (thomas(AT)ahle.dk), Aug 15 2011
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