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A036917
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a(n) = (16*(n-1/2)*(2*n^2-2*n+1)*a(n-1)-256*(n-1)^3*a(n-2))/n^3.
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5
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1, 8, 88, 1088, 14296, 195008, 2728384, 38879744, 561787864, 8206324928, 120929313088, 1794924383744, 26802975999424, 402298219288064, 6064992788397568, 91786654611673088, 1393772628452578264, 21227503080738294464, 324160111169327247424
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| M. Petkovsek et al., "A=B", Peters, p. ix of second printing.
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LINKS
| N. J. A. Sloane, My favorite integer sequences, in Sequences and their Applications (Proceedings of SETA '98).
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FORMULA
| Sum(C(2 * n-k, n-k)^2 * C(2 * k, k)^2, k=0..n).
G.f.: (4/Pi^2)*EllipticK(4*x^(1/2))^2. - Vladeta Jovovic (vladeta(AT)eunet.rs), Dec 01 2003
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MATHEMATICA
| a[n_] := (16 (n - 1/2)(2*n^2 - 2*n + 1)a[n - 1] - 256(n - 1)^3 a[n - 2])/n^3; a[0] = 1; a[1] = 8; Array[a, 19, 0] (* Or *)
f[n_] := Sum[(Binomial[2 (n - k), n - k] Binomial[2 k, k])^2, {k, 0, n}]; Array[f, 19, 0] (* Or *)
lmt = 20; Take[ 4^Range[0, 2 lmt]*CoefficientList[ Series[(4/Pi^2) EllipticK[4 x^(1/2)]^2, {x, 0, lmt}], x^(1/2)], lmt] (* RGWv *)
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CROSSREFS
| Cf. A036915, A057703.
Sequence in context: A112907 A053380 A115864 * A003497 A051605 A006750
Adjacent sequences: A036914 A036915 A036916 * A036918 A036919 A036920
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Formula corrected by Tito Piezas III Tito Piezas III (tpiezas(AT)gmail.com), Oct 19 2010
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