0,3

Number of arrangements of 1,2,..,n*n in an n*n matrix such that each row and each column is increasing.

Factor g_n in formula for 2n-th moment of Riemann zeta function on the critical line. (See Conrey article.) - Michael Somos, Apr 15 2003

Number of linear extensions of the n X n lattice. - Mitch Harris (Harris.Mitchell (AT) mgh.harvard.edu), Dec 27, 2005

The problem for a 5 X 5 array was recently posed and solved in the College Mathematics Journal. The solution is in Vol. 30 (1999), no. 5, pp. 410-411.

J. B. Conrey, The Riemann Hypothesis, Notices Amer. Math. Soc., 50 (No. 3, March 2003), 341-353. See p. 349.

J. S. Frame, G. de B. Robinson and R. M. Thrall, The hook graphs of a symmetric group, Canad. J. Math. 6 (1954), pp. 316-324.

M. du Sautoy, The Music of the Primes, Fourth Estate / HarperCollins, 2003; see p. 284.

J. B. Conrey, The Riemann Hypothesis

Index entries for sequences related to Young tableaux.

a(n) = (n^2)! / (product k=1, ..., 2n-1 k^(n - |n-k|))

a(n) = 0!*1!*..*(k-1)! *(k*n)! / ( n!*(n+1)!*..*(n+k-1)! ) for k=n.

a(n) =A088020(n)/A107254(n) =A088020(n)*A000984(n)/A079478(n). - Henry Bottomley (se16(AT)btinternet.com), May 14 2005

Using the hook length formula, a(4) = (16)!/(7*6^2*5^3*4^4*3^3*2^2) = 24024.

(PARI) a(n)=if(n<0, 0, (n^2)!*prod(k=0, n-1, k!/(n+k)!))

Main diagonal of A060854. a(2)=A000108(2), a(3)=A005789(3), a(4)=A005790(4), a(5)=A005791(5).

Sequence in context: A140170 A038396 A124103 this_sequence A130506 A052078 A069544

Adjacent sequences: A039619 A039620 A039621 this_sequence A039623 A039624 A039625

nonn,nice,easy

Floor van Lamoen (fvlamoen(AT)hotmail.com)

References, correction and extension from Stephen G. Penrice (spenrice(AT)ets.org), Jun 15 2000