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A140901 Number of 3 X 5 matrices with elements in 0..n with each row and each column in nondecreasing order. 3,5,n can be permuted, see formula. 1
1, 56, 1176, 14112, 116424, 731808, 3737448, 16195608, 61408347, 208416208, 644195552, 1837984512, 4892876352, 12259074816, 29115302688, 65937597264, 143107211709, 298915373064, 603074875480, 1178943365600, 2239226847000, 4142127132000, 7477931097000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

Jonas Wallgren, Arie Groeneveld, and Franklin T. Adams-Watters

W. F. Wheatley and James Ethridge (Proposers), Comment from Alan H. Rapoport, Problem 84, Missouri Journal of Mathematical Sciences, volume 8, #2, Spring 1996, pages 97-102.

LINKS

Table of n, a(n) for n=0..22.

FORMULA

(Empirical) set p,q,r to n,5,3 (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)).

(Conjecture) G.f.: (1+40*x+400*x^2+1456*x^3+2212*x^4+1456*x^5+400*x^6+40*x^7+x^8)/(1-x)^16. [Bruno Berselli, May 08 2012]

CROSSREFS

Sequence in context: A219583 A341429 A002009 * A160346 A219371 A183587

Adjacent sequences:  A140898 A140899 A140900 * A140902 A140903 A140904

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jul 05 2008

STATUS

approved

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Last modified December 2 02:12 EST 2021. Contains 349435 sequences. (Running on oeis4.)