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%I #19 May 05 2022 04:41:59
%S 1,5,45,544,8125,143856,2941225,68157440,1764915561,50500000000,
%T 1582182900661,53868106874880,1980337235410885,78180905165533184,
%U 3298800640869140625,148150413341979836416,7055872821971695929745,355210628457538186444800
%N a(n) = (n^(n+1) + n^(n-1))/2.
%C a(n) is the number of monotonic runs over all length n words on an alphabet of n letters. - _Geoffrey Critzer_, Jun 25 2013
%H Harry J. Smith, <a href="/A062023/b062023.txt">Table of n, a(n) for n = 1..100</a>
%F E.g.f.: (-1/2)*LambertW(-x)*(1 + 1/(1 + LambertW(-x))^3). - _G. C. Greubel_, May 04 2022
%e a(3) = {3^4 +3^2}/2 = 45.
%t Table[(n^(n-1)+n^(n+1))/2,{n,1,20}] (* _Geoffrey Critzer_, Jun 25 2013 *)
%o (PARI) { for (n=1, 30, write("b062023.txt", n, " ", (n^(n+1) + n^(n-1))/2) ) } \\ _Harry J. Smith_, Jul 29 2009
%o (SageMath) [(n^(n+1) + n^(n-1))/2 for n in (1..20)] # _G. C. Greubel_, May 04 2022
%Y Cf. A229078.
%K nonn
%O 1,2
%A _Amarnath Murthy_, Jun 02 2001
%E More terms from Larry Reeves (larryr(AT)acm.org), Jun 06 2001
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