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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
Richard P. Stanley: Enumerative Combinatorics, vol. 2, p. 378.
LINKS
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.
FORMULA
(Empirical) Set p,q,r to n,5,3 (in any order) in s=p+q+r-1; a(n) = Product_{i=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
a(n) = Product_{i=1..3} Product_{j=1..5} Product_{k=1..n+1} (i + j + k - 1) / (i + j + k - 2). See the section on plane partitions with bounded part size in Stanley's reference. This comment is relevant to the sequences A140902 - A140943 as well. - Sela Fried, Oct 18 2023
CROSSREFS
Sequence in context: A219583 A341429 A002009 * A160346 A219371 A183587
KEYWORD
nonn
AUTHOR
R. H. Hardin, Jul 05 2008
STATUS
approved

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Last modified July 23 19:43 EDT 2024. Contains 374553 sequences. (Running on oeis4.)