A013699 Degree of variety K_{2,n}^2.

1, 32, 610, 9842, 147798, 2145600, 30664890, 435668420, 6186432967, 88066807556, 1258885297696, 18084694597452, 261164661944060, 3791317346771584, 55316720239735242, 810944384733610356

Offset: 1

Author

Joachim.Rosenthal(AT)nd.edu (Joachim Rosenthal)

Keywords

• nonn
• easy

Comments

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).

Links

• M. S. Ravi et al., Dynamic pole assignment and Schubert calculus, SIAM J. Control Optimization, 34 (1996), 813-832, esp. p. 825.

Crossrefs

Cf. A013698 (q=1), A013700 (q=3), A013701 (q=4), A013702 (q=5).

Programs

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))!)