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%I #19 Sep 24 2023 09:15:43
%S 1,2,4,10,28,72,198,572,1560,4420,12920,36176,104006,305900,869400,
%T 2521260,7443720,21360240,62300700,184410072,532740208,1560167752,
%U 4626704368,13432367520,39457579590,117177054540,341487416088,1005490725148,2989296750440,8737944347440,25776935824948
%N a(n) is the smallest entry of the n-th column of the matrix of Super Catalan numbers S(m,n).
%C Super Catalan number S(m,n) is [(2m)! (2n)! ] / [(m!) (n!) (m+n)! ], where m,n are nonnegative integers.
%C S(m,n) is a positive integer, but a combinatorial interpretation of S(m,n) is an open problem.
%C For each n, the sequence S(m,n) is decreasing then increasing, with minimum value at m = ceiling(n/3).
%C Our sequence is that list of values S( ceiling(n/3), n).
%C S(n,k-n) = C(2k,k) * C(k,n) / C(2k,2n). - _Charlie Neder_, Dec 27 2018
%H Seiichi Manyama, <a href="/A173781/b173781.txt">Table of n, a(n) for n = 0..2099</a>
%H Ira M. Gessel, <a href="http://people.brandeis.edu/~gessel/homepage/papers/superballot.pdf">Super ballot numbers</a>, J. Symbolic Comp., 14 (1992), 179-194.
%H Ira M. Gessel and Guoce Xin, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL8/Gessel/xin.html">A Combinatorial Interpretation of the Numbers 6(2n)!/n!(n+2)!</a>, Journal of Integer Sequences, Vol. 8 (2005), Article 05.2.3, 13 pp.
%F a(3*n) = A211419(n). - _Peter Bala_, Sep 24 2023
%t nn = 30; {1}~Join~Table[Min@ Map[Function[n, ((2 m)! (2 n)!)/((m!) (n!) (m + n)!)], Range@ nn], {m, nn}] (* _Michael De Vlieger_, Jul 16 2016 *)
%Y Cf. A211419.
%K easy,nonn
%O 0,2
%A Joseph Alfano (jalfano(AT)assumption.edu), Feb 24 2010
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