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A049503 a(n) = A005130(n)^2. 5
1, 1, 4, 49, 1764, 184041, 55294096, 47675849104, 117727187246656, 831443906113411600, 16779127803917965290000, 966945347924006310543140625, 159045186822042363450404006250000, 74638947576233124529271587010756250000, 99910846988474589225795290311922220324000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Expansion of generating function A_{QT}^(1)(4n).

a(n) is the number of cyclically symmetric and self-complementary plane partitions in a (2n)-cube. - Peter J. Taylor, Jun 17 2015

REFERENCES

D. M. Bressoud, Proofs and Confirmations, Camb. Univ. Press, 1999; Eq. (6.16), p. 199.

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..66

M. Ciucu, The equivalence between enumerating cyclically symmetric, self-complementary and totally symmetric, self-complementary plane partitions, J. Combin. Theory Ser. A 86 (1999), 382-389.

G. Kuperberg, Symmetries of plane partitions and the permanent-determinant method, J. Comb. Theory Ser. A, 68 (1994), 115-151. [From Peter J. Taylor, Jun 17 2015]

G. Kuperberg, Symmetry classes of alternating-sign matrices under one roof, arXiv:math/0008184 [math.CO], 2000-2001. [Th. 5].

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

Wikipedia, Plane partition

FORMULA

a(n) = 2^n * det U(n), where U(n) is the n X n matrix with entry (i, j) equal to binomial(i+j, 2*i-j)/2+binomial(i+j, 2*i-j-1). [Ciucu]

MATHEMATICA

f[n_]:=Product[((3 k + 1)!/(n + k)!)^2, {k, 0, n-1}]; Table[f[n], {n, 0, 15}] (* Vincenzo Librandi, Jun 18 2015 *)

PROG

(PARI) a(n) = 2^n*matdet(matrix(n, n, i, j, i--; j--; binomial(i+j, 2*i-j)/2+binomial(i+j, 2*i-j-1))); \\ Michel Marcus, Jun 18 2015

(MAGMA) [n eq 0 select 1 else &*[(Factorial(3*k+1)/Factorial(n+k))^2: k in [0..n-1]]: n in [0..15]]; // Bruno Berselli, Jun 23 2015

CROSSREFS

Cf. A005130.

Sequence in context: A029991 A129419 A212130 * A159593 A263441 A067717

Adjacent sequences:  A049500 A049501 A049502 * A049504 A049505 A049506

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified November 19 02:01 EST 2018. Contains 317332 sequences. (Running on oeis4.)