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Number of standard Young tableaux of n cells and height >= 10.
2

%I #15 Jun 09 2023 22:04:39

%S 1,11,121,1001,8086,59228,426673,2946593,20161558,135303408,904408398,

%T 5995379358,39727129830,262629161094,1739604051411,11535387587595,

%U 76763703224070,512448824337780,3436760740882050,23151339236295810,156789753069685500,1067435349046248600

%N Number of standard Young tableaux of n cells and height >= 10.

%C Also number of self-inverse permutations in S_n with longest increasing subsequence of length >= 10.

%H Alois P. Heinz, <a href="/A218262/b218262.txt">Table of n, a(n) for n = 10..300</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Involution_(mathematics)">Involution (mathematics)</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Young_tableau">Young tableau</a>

%F a(n) = A000085(n) - A212915(n) = A182172(n,n) - A182172(n,9).

%Y Column k=10 of A182222.

%Y Cf. A000085, A212915, A182172.

%K nonn

%O 10,2

%A _Alois P. Heinz_, Oct 24 2012