A013701 Degree of variety K_{2,n}^4.

1, 512, 75025, 7174454, 562110290, 39541748736, 2610763825782, 165745451110910, 10262482704258873, 625250747214775916, 37701606156514031251, 2258713106034310399852, 134810129909509070121060

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 6n+8 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), A013699 (q=2), A013700 (q=3), A013702 (q=5).

Programs

PARI

K(n,q=4)=(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))!)