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%I #10 Aug 21 2020 09:09:12
%S 1,32,610,9842,147798,2145600,30664890,435668420,6186432967,
%T 88066807556,1258885297696,18084694597452,261164661944060,
%U 3791317346771584,55316720239735242,810944384733610356
%N Degree of variety K_{2,n}^2.
%C Number of Catalan paths (nonnegative, starting and ending at 0, step +/-1) of 4n+4 steps with all values less than or equal to n+1 (see A080934).
%H M. S. Ravi et al., <a href="https://doi.org/10.1137/S036301299325270X">Dynamic pole assignment and Schubert calculus</a>, SIAM J. Control Optimization, 34 (1996), 813-832, esp. p. 825.
%o (PARI) K(n,q=2)=(2*n+n*q+2*q)!*sum(j=0,q,((q-2*j)*(n+2)+1)/(n+j*(n+2))!/(n+1+(q-j)*(n+2))!)
%Y Cf. A013698 (q=1), A013700 (q=3), A013701 (q=4), A013702 (q=5).
%K nonn,easy
%O 1,2
%A Joachim.Rosenthal(AT)nd.edu (Joachim Rosenthal)
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