%I #8 Dec 09 2016 06:20:38
%S 1,2,4,9,24,75,269,1095,5039,26084,150356,952526,6553011,48553418,
%T 385693800,3277413802,29741002168,287555932433,2952769116993,
%U 32079033571080,367336668735826,4419518218479215,55733223965845539,735448682261126767,10142738983005750681
%N Antidiagonals of table A047888 (which counts longest increasing subsequences and pattern avoidances).
%C Note that:
%C A000108 avoids string "123"
%C A005808 avoids string "1234"
%C A047889 avoids string "12345"
%C Note also that the left half and central diagonal of A047888 are partial sums of table A047874.
%e We can write A141824(n) = 1 2 4 9 24 ... because A047888 begins
%e 1;
%e 1, 1;
%e 1, 2, 1;
%e 1, 5, 2, 1;
%e 1, 14, 6, 2, 1;
%e etc.
%Y Cf. A000108 (Catalan numbers), A005808, A047889, A047874.
%K nonn
%O 1,2
%A _Alford Arnold_, Jul 08 2008
%E a(12)-a(25) from _Alois P. Heinz_, Apr 10 2012