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

0,2

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

Table of n, a(n) for n=0..20.

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)

Crossrefs

Cf. A001263, A134291, A140925.

Sequence in context: A172217 A036524 A262063 * A133239 A210407 A146479

Adjacent sequences: A140931 A140932 A140933 * A140935 A140936 A140937

Keyword

nonn

Author

R. H. Hardin, Jul 05 2008

Status

approved