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A002897 C(2n,n)^3.
(Formerly M4580 N1952)
18
1, 8, 216, 8000, 343000, 16003008, 788889024, 40424237568, 2131746903000, 114933031928000, 6306605327953216, 351047164190381568, 19774031697705428416, 1125058699232216000000, 64561313052442296000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

C. Domb, On the theory of cooperative phenomena in crystals, Advances in Phys., 9 (1960), 149-361.

S. Ramanujan, Modular Equations and Approximations to pi, pp. 23-39 of Collected Papers of Srinivasa Ramanujan, Ed. G. H. Hardy et al., AMS Chelsea 2000. See page 36, equation (25).

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..100

David H. Bailey, Jonathan M. Borwein, David Broadhurst and M. L. Glasser, Elliptic integral evaluations of Bessel moments, arXiv:0801.0891.

FORMULA

Expansion of (K(k)/(Pi/2))^2 in powers of (kk'/4)^2, where K(k) is complete elliptic integral of first kind evaluated at modulus k. - Michael Somos, Jan 31 2007

G.f.: F(1/2, 1/2, 1/2; 1, 1; 64x) where F() is a hypergeometric function. - Michael Somos, Jan 31 2007

G.f.: hypergeom([1/4,1/4],[1],64*x)^2. - Mark van Hoeij, Nov 17 2011

n^3*a(n) -8*(2*n-1)^3*a(n-1)=0. - R. J. Mathar, Mar 08 2013

MATHEMATICA

a[n_]:= Coefficient[ Series[ HypergeometricPFQ[ {1/2, 1/2, 1/2}, {1, 1}, 64x], {x, 0, n}], x, n]

PROG

(PARI) {a(n)= binomial(2*n, n)^3} /* Michael Somos, Jan 31 2007 */

(Sage) [binomial(2*n, n)**3 for n in xrange(0, 17)] # Zerinvary Lajos, Apr 21 2009

(MAGMA) [Binomial(2*n, n)^3: n in [0..20]]; // Vincenzo Librandi, Nov 18 2011

CROSSREFS

Sequence in context: A069045 A123057 A009072 * A024289 A009106 A000442

Adjacent sequences:  A002894 A002895 A002896 * A002898 A002899 A002900

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Simon Plouffe

STATUS

approved

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Last modified December 18 07:26 EST 2014. Contains 252098 sequences.