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A049505 a(n) = Product_{1<=i<=j<=n} (i+j+n-1)/(i+j-1), number of symmetric plane partitions in n-cube. 6
1, 2, 10, 112, 2772, 151008, 18076916, 4751252480, 2740612658576, 3468301123758080, 9627912669442441500, 58618653300361405440000, 782683432110638830001250000, 22916694891747599820616089600000, 1471328419282772010324439370939640000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The first printing of the Bressoud book states that the formula Product_{1<=i<=j<=n} (i+j+n-1)/(i+j-1) in Eq. (6.8) is the number of totally symmetric plane partitions. This is wrong, although it does produce the current sequence. For the correct formula for the number of totally symmetric plane partitions see A005157.

REFERENCES

D. M. Bressoud, Proofs and Confirmations, Camb. Univ. Press, 1999; Eq. (6.8), p. 198.

LINKS

T. D. Noe, Table of n, a(n) for n=0..40

P. J. Taylor, Counting distinct dimer hex tilings, Preprint, 2015.

FORMULA

a(n) = product_{1<=i<=j<=n} (i+j+n-1)/(i+j-1).

a(n) = product_{1<=i<=n} (((2*i-2)!*(i+2*n-1)!)/((i+n-1)!*(2*i+n-2)!)). - Jean-François Alcover, Jun 22 2012.

a(n) = product_{1<=i<=n} (binomial((i-1) + 2*n, n)/binomial(n + 2*(i-1), n)). - Olivier Gérard, Feb 25 2015.

a(n) ~ exp(1/24) * 3^(9*n^2/4 + 3*n/4 - 1/24) / (A^(1/2) * n^(1/24) * 2^(3*n^2 + n/2 + 1/8)), where A = A074962 = 1.2824271291... is the Glaisher-Kinkelin constant. - Vaclav Kotesovec, Mar 01 2015

MAPLE

A049505 := proc(n) local i, j; mul(mul((i+j+n-1)/(i+j-1), j=i..n), i=1..n); end;

MATHEMATICA

a[n_] := Product[ ((2i-2)!*(i+2n-1)!)/((i+n-1)!*(2i+n-2)!), {i, 1, n}]; Table[a[n], {n, 0, 14}] (* Jean-François Alcover, Jun 22 2012, after PARI *)

PROG

(PARI) a(n)=prod(i=1, n, prod(j=i, n, (i+j+n-1)/(i+j-1)))

CROSSREFS

Main diagonal of array A102539.

Main diagonal of array in A073165.

Cf. A005157, A008793.

Sequence in context: A062499 A305854 A234296 * A136518 A168369 A317342

Adjacent sequences:  A049502 A049503 A049504 * A049506 A049507 A049508

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Edited by N. J. A. Sloane, Jun 30 2013. Codes and formula checked by N. J. A. Sloane and Olivier Gérard.

STATUS

approved

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Last modified November 18 19:59 EST 2019. Contains 329288 sequences. (Running on oeis4.)