A140934 Number of 2 X 11 matrices with elements in 0..n with each row and each column in nondecreasing order. 2,11,n can be permuted, see formula.

1, 78, 2366, 41405, 496860, 4504864, 32821152, 200443464, 1057896060, 4936848280, 20734762776, 79483257308, 281248448936, 927192688800, 2869882132000, 8394405236100, 23331508670925, 61912369414350, 157496378334750, 385451662766625, 910400117772600

Offset: 0

Author

R. H. Hardin, Jul 05 2008

Keywords

• nonn

Comments

In the definition, 2,11,n can be permuted, see formula.

Conjecture: 12th column (and diagonal) of the triangle A001263. - Bruno Berselli, May 07 2012

References

• S. Mukai, An Introduction to Invariants and Moduli, Cambridge, 2003; Prop. 8.4, case n=13. - N. J. A. Sloane, Aug 28 2010.

Links

• Feihu Liu, Guoce Xin, and Chen Zhang, Ehrhart Polynomials of Order Polytopes: Interpreting Combinatorial Sequences on the OEIS, arXiv:2412.18744 [math.CO], 2024. See pp. 1, 3, 25, 27.

Crossrefs

Cf. A001263, A134291, A140925.

Formula

Empirical: Set p,q,r to n,11,2 (in any order) in s=p+q+r-1; a(n) = product {i in 0..r-1} (binomial(s,p+i)*i!/(s-i)^(r-i-1))

G.f. conjectured: (1 + 55*x + 825*x^2 + 4950*x^3 + 13860*x^4 + 19404*x^5 + 13860*x^6 + 4950*x^7 + 825*x^8 + 55*x^9 + x^10)/(1 - x)^23. - Bruno Berselli, May 07 2012

Conjecture: a(n) = ((n+12)/(12*n+12))*binomial(n+11,11)^2. - Bruno Berselli, May 07 2012

Conjecture: a(n) = Product_{i=1..11} A002378(n+i)/A002378(i). - Bruno Berselli, Sep 01 2016

From Amiram Eldar, Oct 19 2020: (Start)

Conjecture: Sum_{n>=0} 1/a(n) = 3538258540001/8820 - 40646320*Pi^2.

Conjecture: Sum_{n>=0} (-1)^n/a(n) = 1678950598/2205 - 23068672*log(2)/21. (End)