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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
1, 78, 2366, 41405, 496860, 4504864, 32821152, 200443464, 1057896060, 4936848280, 20734762776, 79483257308, 281248448936, 927192688800, 2869882132000, 8394405236100, 23331508670925, 61912369414350, 157496378334750, 385451662766625, 910400117772600 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 23 23:39 EDT 2021. Contains 345403 sequences. (Running on oeis4.)