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 A062023 a(n) = (n^(n+1) + n^(n-1))/2. 4
 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)
 OFFSET 1,2 COMMENTS a(n) is the number of monotonic runs over all length n words on an alphabet of n letters. - Geoffrey Critzer, Jun 25 2013 LINKS Harry J. Smith, Table of n, a(n) for n = 1..100 FORMULA E.g.f.: (-1/2)*LambertW(-x)*(1 + 1/(1 + LambertW(-x))^3). - G. C. Greubel, May 04 2022 EXAMPLE a(3) = {3^4 +3^2}/2 = 45. MATHEMATICA Table[(n^(n-1)+n^(n+1))/2, {n, 1, 20}] (* Geoffrey Critzer, Jun 25 2013 *) PROG (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 CROSSREFS Cf. A229078. Sequence in context: A248586 A275576 A189122 * A169714 A084095 A174495 Adjacent sequences: A062020 A062021 A062022 * A062024 A062025 A062026 KEYWORD nonn AUTHOR Amarnath Murthy, Jun 02 2001 EXTENSIONS More terms from Larry Reeves (larryr(AT)acm.org), Jun 06 2001 STATUS approved

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Last modified April 2 01:40 EDT 2023. Contains 361723 sequences. (Running on oeis4.)