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A069080
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a(n) = (2n+1)*(2n+2)*(2n+6)*(2n+7).
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1
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84, 864, 3300, 8736, 18900, 35904, 62244, 100800, 154836, 228000, 324324, 448224, 604500, 798336, 1035300, 1321344, 1662804, 2066400, 2539236, 3088800, 3722964, 4449984, 5278500, 6217536, 7276500, 8465184, 9793764, 11272800, 12913236, 14726400, 16724004
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OFFSET
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0,1
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REFERENCES
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Konrad Knopp, Theory and application of infinite series, Dover, p. 268.
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LINKS
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FORMULA
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Sum_{n>=0} (-1)^n/a(n) = (Pi-149/60)/60. [Corrected by Amiram Eldar, Mar 08 2022]
G.f.: 12*(7 + 37*x - 15*x^2 + 3*x^3) / (1 - x)^5.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).
a(n) = 16*n^4 + 128*n^3 + 332*n^2 + 304*n + 84. (End)
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MAPLE
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MATHEMATICA
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CoefficientList[Series[12 (7 + 37x - 15x^2 + 3x^3)/(1 - x)^5, {x, 0, 30}], x] (* Wesley Ivan Hurt, Mar 28 2015 *)
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PROG
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(Magma) [(2*n+1)*(2*n+2)*(2*n+6)*(2*n+7) : n in [0..30]]; // Wesley Ivan Hurt, Mar 28 2015
(PARI) Vec(12*(7 + 37*x - 15*x^2 + 3*x^3) / (1 - x)^5 + O(x^50)) \\ Michel Marcus, Mar 29 2015
(PARI) vector(50, n, n--; (2*n+1)*(2*n+2)*(2*n+6)*(2*n+7)) \\ Michel Marcus, Mar 29 2015
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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