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A164102
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Decimal expansion of 2*Pi^2.
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13
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1, 9, 7, 3, 9, 2, 0, 8, 8, 0, 2, 1, 7, 8, 7, 1, 7, 2, 3, 7, 6, 6, 8, 9, 8, 1, 9, 9, 9, 7, 5, 2, 3, 0, 2, 2, 7, 0, 6, 2, 7, 3, 9, 8, 8, 1, 4, 4, 8, 1, 5, 8, 1, 2, 5, 2, 8, 2, 6, 6, 9, 8, 7, 5, 2, 4, 4, 0, 0, 8, 9, 6, 4, 4, 8, 3, 8, 4, 1, 0, 4, 8, 6, 0, 0, 3, 5, 4, 6, 8, 0, 7, 4, 3, 7, 1, 0, 4, 4, 6, 3, 6, 4, 8, 0
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OFFSET
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2,2
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COMMENTS
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Surface area of the 4-dimensional unit sphere. The volume of the 4-dimensional unit sphere is a fourth of this, A102753.
Also decimal expansion of Pi^2/5 = 1.973920..., with offset 1. - Omar E. Pol, Oct 04 2011
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REFERENCES
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L. A. Santalo, Integral Geometry and Geometric Probability, Addison-Wesley, 1976, see p. 15.
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LINKS
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H.-J. Seiffert, Problem B-705, Elementary Problems and Solutions, The Fibonacci Quarterly, Vol. 29, No. 4 (1991), p. 372; An Application of a Series Expansion for (arcsinx)^2, Solution to Problem B-705, ibid., Vol. 31, No. 1 (1993), pp. 85-86.
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FORMULA
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Pi^2/5 = Sum_{k>=1} Lucas(2*k)/(k^2*binomial(2*k,k)) = Sum_{k>=1} A005248(k)/A002736(k) (Seiffert, 1991). - Amiram Eldar, Jan 17 2022
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EXAMPLE
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19.739208802178717237668981...
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MATHEMATICA
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PROG
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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