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A002897
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C(2n,n)^3.
(Formerly M4580 N1952)
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18
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1, 8, 216, 8000, 343000, 16003008, 788889024, 40424237568, 2131746903000, 114933031928000, 6306605327953216, 351047164190381568, 19774031697705428416, 1125058699232216000000, 64561313052442296000000
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OFFSET
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0,2
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REFERENCES
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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).
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LINKS
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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.
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FORMULA
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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
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MATHEMATICA
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a[n_]:= Coefficient[ Series[ HypergeometricPFQ[ {1/2, 1/2, 1/2}, {1, 1}, 64x], {x, 0, n}], x, n]
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PROG
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(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
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CROSSREFS
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Sequence in context: A069045 A123057 A009072 * A024289 A009106 A000442
Adjacent sequences: A002894 A002895 A002896 * A002898 A002899 A002900
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane, Simon Plouffe
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STATUS
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approved
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