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Number of up-down parking functions of length n.
1

%I #18 Nov 29 2015 13:45:06

%S 1,1,1,4,17,120,915,9470,104436,1432713,20709209,354493902,6343919118,

%T 130255212146,2780356513594,66607482974307,1651884203936474,

%U 45240390673466869,1278413274487999471,39403978336643657797,1249821733374560346851,42820844948653526713511

%N Number of up-down parking functions of length n.

%C A parking function (c_1, c_2, c_3, c_4, c_5 ..., c_n) is up-down if c_1 < c_2 > c_3 < c_4 > c_5... .

%C Clearly, A000111(n) <= a(n) <= A000272(n+1).

%F a(2n) = A264963(2n). - _Alois P. Heinz_, Nov 29 2015

%e For n = 3, the a(3) = 4 up-down parking functions are (1,3,1), (1,2,1), (1,3,2), (2,3,1).

%Y Cf. A000111, A000272, A264963.

%K nonn

%O 0,4

%A _Ran Pan_, Nov 16 2015

%E a(0),a(10)-a(21) from _Alois P. Heinz_, Nov 25 2015, Nov 29 2015