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A014062
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a(n) = binomial(n^2, n).
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46
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1, 1, 6, 84, 1820, 53130, 1947792, 85900584, 4426165368, 260887834350, 17310309456440, 1276749965026536, 103619293824707388, 9176358300744339432, 880530516383349192480, 91005567811177478095440, 10078751602022313874633200, 1190739044344491048895397910
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OFFSET
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0,3
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COMMENTS
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Roberts states that Gupta and Khare show that a(n) > A002110(n) for 2 < n < 1794 and that a(n) < A002110(n) for n >= 1794, where A002110(n) is the product of the first n primes. - T. D. Noe, Oct 03 2007
This sequence describes the number of ways to arrange n objects in an n X n array (for example, stars in a flag's field pattern). - Tom Young (mcgreg265(AT)msn.com), Jun 17 2010
It appears that a(n) == n (mod n^3) only if n is 1, an odd prime, the square of an odd prime, or the cube of an odd prime. - Gary Detlefs, Aug 06 2013; corrected by Michel Marcus, May 29 2015
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REFERENCES
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J. Roberts, Lure of the Integers, Math. Assoc. America, 1992, p. 265.
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LINKS
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FORMULA
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a(n) = Sum_{k=0..n} binomial(n, k) * binomial(n^2 - n, k). - Paul D. Hanna, Nov 18 2015
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MATHEMATICA
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PROG
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(PARI) {a(n) = sum(k=0, n, binomial(n, k)*binomial(n^2-n, k))}
(Magma) [Binomial(n^2, n): n in [0..30]]; // G. C. Greubel, Apr 29 2024
(SageMath) [binomial(n^2, n) for n in range(31)] # G. C. Greubel, Apr 29 2024
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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