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%I #11 Oct 28 2020 17:55:49
%S 1,1,1,2,3,5,11,23,50,118,283,731,1921,5370,14884,43118,130509,397490,
%T 1266010,4077494,13435445,45687806,157483627,551205779,1979511990
%N a(n) is the number of length-n ballot sequences whose reversals are also ballot sequences.
%C Ballot sequences B have positive terms, and for any finite prefix P of B and any k > 0, the number of occurrences of k in P is greater than or equal to the number of occurrences of k+1 in P.
%H Rémy Sigrist, <a href="/A338418/a338418.txt">C++ program for A338418</a>
%F a(n) >= A338417(n).
%e For n = 5:
%e - the reversals of the following length-5 ballot sequences are also ballot sequences:
%e (1, 1, 1, 1, 1)
%e (1, 1, 1, 2, 1)
%e (1, 1, 2, 1, 1)
%e (1, 2, 1, 1, 1)
%e (1, 2, 1, 2, 1)
%e - so a(5) = 5.
%o (C++) See Links section.
%Y Cf. A000085, A167510, A338417.
%K nonn,more
%O 0,4
%A _Rémy Sigrist_, Oct 25 2020
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