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A005419
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Number of nonequivalent dissections of a polygon into n heptagons by nonintersecting diagonals up to rotation and reflection.
(Formerly M3023)
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6
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1, 1, 3, 16, 112, 1020, 10222, 109947, 1230840, 14218671, 168256840, 2031152928, 24931793768, 310420597116, 3912823963482, 49853370677834, 641218583442360, 8316918403772790, 108686334145327785, 1429927553582849256, 18927697628428129728, 251931892228273729375
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OFFSET
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1,3
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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See Mathematica code.
a(n) ~ 2^(6*n - 1) * 3^(6*n + 1/2) / (sqrt(Pi) * n^(5/2) * 5^(5*n + 5/2)). - Vaclav Kotesovec, Mar 13 2016
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MATHEMATICA
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p=7; Table[(Binomial[(p-1)n, n]/(((p-2)n+1)((p-2)n+2)) + If[OddQ[n], If[OddQ[p], Binomial[(p-1)n/2, (n-1)/2]/n, (p+1)Binomial[((p-1)n-1)/2, (n-1)/2]/((p-2)n+2)], 3Binomial[(p-1)n/2, n/2]/((p-2)n+2)]+Plus @@ Map[EulerPhi[ # ]Binomial[((p-1)n+1)/#, (n-1)/# ]/((p-1)n+1)&, Complement[Divisors[GCD[p, n-1]], {1, 2}]])/2, {n, 1, 20}] (* Robert A. Russell, Dec 11 2004 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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