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A125143
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Almkvist-Zudilin numbers: Sum_{k=0..n} (-1)^(n-k) * ((3^(n-3*k) * (3*k)!) / (k!)^3) * binomial(n,3*k) * binomial(n+k,k).
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1
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1, -3, 9, -3, -279, 2997, -19431, 65853, 292329, -7202523, 69363009, -407637387, 702049401, 17222388453, -261933431751, 2181064727997, -10299472204311, -15361051476987, 900537860383569, -10586290198314843, 74892552149042721, -235054958584593843
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| Almkvist, Gert; Krattenthaler, Christian; and Petersson, Joakim; Some new formulas for pi. Experiment. Math. 12 (2003), 441-456. (Math Rev MR2043994 by W. Zudilin)
Heng Huat Chan and Helena Verrill, The Apery numbers, the Almkvist-Zudilin numbers and new series for 1/Pi, Math. Res. Lett. 16 (2009), no. 3, 405-420.
Helena Verrill, in a talk at the annual meeting of the Amer. Math. Soc., New Orleans, LA, Jan 2007 on "Series for 1/pi".
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LINKS
| Arkadiusz Wesolowski, Table of n, a(n) for n = 0..200
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FORMULA
| a(n) = sum(k=0..n, (-1)^(n-k) * ((3^(n-3*k) * (3*k)!) / (k!)^3) * binomial(n,3*k) * binomial(n+k,k) ). [Arkadiusz Wesolowski, Jul 13 2011]
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PROG
| (PARI) a(n) = sum(k=0, n, (-1)^(n-k)*((3^(n-3*k)*(3*k)!)/(k!)^3)*binomial(n, 3*k)*binomial(n+k, k) ).
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CROSSREFS
| Sequence in context: A120429 A101431 A120982 * A200012 A130701 A197507
Adjacent sequences: A125140 A125141 A125142 * A125144 A125145 A125146
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KEYWORD
| easy,sign
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AUTHOR
| R. K. Guy, Jan 11 2007
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EXTENSIONS
| Edited and more terms added by Arkadiusz Wesolowski, Jul 13 2011
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