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A244148 The number of ways one can assign values to n arrays a_{1},...,a_{n} of increasing size (size of a_{1} is 1, size of a_{2} is 2, ..., size of a_{n} is n) using the numbers 1, ..., n*(n+1)/2, distinctly, such that the positions of array a_{i} can only be assigned values in the interval ((n+1)-i),... , (n*(n+1)/2-(n-i)). 1
1, 2, 72, 115200, 13276569600, 165253252792320000, 312379127174190543667200000, 120053472861445542607502662277529600000, 12098873398276702490569569159619238449643520000000000, 400639807706466477973460949403651522366500906696560470917120000000000 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
This sequence provides an upper bound for the following sequence: the number of ways one can assign values to n arrays a_{1},...,a_{n} of increasing size (size of a_{1} is 1, size of a_{2} is 2, ..., size of a_{n} is n) using the numbers 1, ..., n*(n+1)/2, distinctly, such that for the j^th position of array a_{i} (a_{i}(j)) one of the follow holds, a_{i+1}(j+1) < a_{i}(j) < a_{i+1}(j) or a_{i+1}(j) < a_{i}(j) < a_{i+1}(j+1). Currently, there is no formula known for enumerating this sequence.
LINKS
Clark Kimberling, Unsolved Problems and Rewards:   Number 18
FORMULA
a(n) = Prod_{k=1..n} (k!* binomial((n^2 - 3*n + 5*k - k^2)/2 , k)).
PROG
(PARI) a(n)=prod(k=1, n, k!* binomial((n^2 - 3*n + 5*k - k^2)/2 , k)); \\ Joerg Arndt, Jun 22 2014
CROSSREFS
Sequence in context: A062082 A067689 A308941 * A320443 A079478 A367492
KEYWORD
easy,nonn
AUTHOR
David M. Cerna, Jun 21 2014
STATUS
approved

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Last modified May 23 17:39 EDT 2024. Contains 372765 sequences. (Running on oeis4.)