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A082635 Square array read by antidiagonals: degree of the K(2,p)^q variety.

%I A082635 #10 Aug 21 2020 09:12:17
%S A082635 1,2,1,5,8,1,14,55,32,1,42,364,610,128,1,132,2380,9842,6765,512,1,429,
%T A082635 15504,147798,265720,75025,2048,1,1430,100947,2145600,9112264,7174454,
%U A082635 832040,8192,1,4862,657800,30664890,290926848,562110290,193710244
%N A082635 Square array read by antidiagonals: degree of the K(2,p)^q variety.
%C A082635 Numbers are related to the dynamic pole assignment problem. "The variety K(m,p)^q can also be viewed as the parameterization of the space of rational curves of degree q of the Grassmann variety Grass(m,m+p)".
%C A082635 Also lim(n->inf, T(n+1,2i)/T(n,2i)) = 4^(i+1).
%H A082635 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.
%F A082635 degK2(p, q)=(-1)^q*(2p+pq+2q)!*sum(j=0, q, ((q-2j)(p+2)+1)/(p+j(p+2))!/(p+1+(q-j)(p+2))!).
%e A082635 Top left corner of array:
%e A082635 1,2,5,14,42,132,429,1430,... A000108 (Catalan numbers)
%e A082635 1,8,55,364,2380,15504,100947,...A013068 deg K(2,n)^1
%e A082635 1,32,610,9842,147798,2145600,...A013069 deg K(2,n)^2
%e A082635 1,128,6765,265720,9112264,... A013070 deg K(2,n)^3
%e A082635 1,512,75025,7174454,... A013071 deg K(2,n)^4
%Y A082635 Cf. A013702.
%Y A082635 Second column is A004171(q), third is A000045(5q).
%Y A082635 T(n, 2i) = A080934((i+1)n+2i, n+1).
%K A082635 nonn,tabl,easy
%O A082635 1,2
%A A082635 _Ralf Stephan_, May 14 2003