

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
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OFFSET

0,2


REFERENCES

Jonas Wallgren, Arie Groeneveld, and Franklin T. AdamsWatters
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 97102.


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+r1; a(n) = product {i in 0..r1} (binomial(s,p+i)*i!/(si)^(ri1)).
(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)/(1x)^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



