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Total number of peaks in all permutations of 2 indistinguishable copies of 1..n.
3

%I #9 May 20 2020 02:43:40

%S 0,3,105,4620,283500,23700600,2610808200,367783416000,64607286744000,

%T 13859305059600000,3567385122341040000,1085582734152396480000,

%U 385634331725066424000000,158175715893528308976000000,74203019661816956710800000000,39481403043334753112451840000000

%N Total number of peaks in all permutations of 2 indistinguishable copies of 1..n.

%H Andrew Howroyd, <a href="/A334776/b334776.txt">Table of n, a(n) for n = 1..100</a>

%F a(n) = Sum_{k=1..n} (k-1)*A334774(n,k).

%F a(n) = A334777(n) - A000680(n).

%o (PARI) \\ PeaksBySig defined in A334774.

%o a(n)={my(u=PeaksBySig(vector(n,i,2), [0..n-1])); sum(k=1, #u, (k-1)*u[k])}

%Y Cf. A000680, A334774, A334775, A334777.

%K nonn

%O 1,2

%A _Andrew Howroyd_, May 12 2020