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A062023
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a(n) = (n^(n+1) + n^(n-1))/2.
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4
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1, 5, 45, 544, 8125, 143856, 2941225, 68157440, 1764915561, 50500000000, 1582182900661, 53868106874880, 1980337235410885, 78180905165533184, 3298800640869140625, 148150413341979836416, 7055872821971695929745, 355210628457538186444800
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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a(n) is the number of monotonic runs over all length n words on an alphabet of n letters. - Geoffrey Critzer, Jun 25 2013
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LINKS
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Harry J. Smith, Table of n, a(n) for n = 1..100
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FORMULA
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E.g.f.: (-1/2)*LambertW(-x)*(1 + 1/(1 + LambertW(-x))^3). - G. C. Greubel, May 04 2022
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EXAMPLE
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a(3) = {3^4 +3^2}/2 = 45.
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MATHEMATICA
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Table[(n^(n-1)+n^(n+1))/2, {n, 1, 20}] (* Geoffrey Critzer, Jun 25 2013 *)
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PROG
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(PARI) { for (n=1, 30, write("b062023.txt", n, " ", (n^(n+1) + n^(n-1))/2) ) } \\ Harry J. Smith, Jul 29 2009
(SageMath) [(n^(n+1) + n^(n-1))/2 for n in (1..20)] # G. C. Greubel, May 04 2022
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CROSSREFS
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Cf. A229078.
Sequence in context: A248586 A275576 A189122 * A169714 A084095 A174495
Adjacent sequences: A062020 A062021 A062022 * A062024 A062025 A062026
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy, Jun 02 2001
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EXTENSIONS
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More terms from Larry Reeves (larryr(AT)acm.org), Jun 06 2001
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STATUS
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approved
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