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Antidiagonals of table A047888 (which counts longest increasing subsequences and pattern avoidances).
2

%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