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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
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
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: A275576 A365564 A189122 * A169714 A084095 A375952
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Jun 02 2001
EXTENSIONS
More terms from Larry Reeves (larryr(AT)acm.org), Jun 06 2001
STATUS
approved