A348371 Decimal expansion of Sum_{k>=0} binomial(2*k,k)^2/(16^k*(k+1)^3).
1, 0, 3, 9, 2, 8, 0, 4, 9, 6, 7, 9, 4, 8, 7, 6, 2, 2, 0, 0, 6, 0, 2, 5, 2, 6, 2, 0, 1, 0, 3, 5, 6, 6, 4, 4, 0, 8, 6, 6, 0, 1, 1, 2, 1, 3, 3, 0, 1, 1, 1, 0, 4, 9, 7, 3, 5, 4, 8, 9, 4, 9, 6, 9, 9, 7, 2, 4, 6, 6, 1, 4, 4, 2, 2, 6, 8, 1, 9, 2, 4, 3, 0, 9, 2, 6, 7, 9, 9, 1, 9, 8, 0, 2, 7, 0, 5, 3, 6, 7, 3, 6, 7, 8, 8
Offset: 1
Examples
1.03928049679487622006025262010356644086601121330111...
Links
- Pablo Fernandez Refolio, Problem 12094, The American Mathematical Monthly, Vol. 126, No. 2 (2019), p. 180; Catalan's Constant from Catalan Numbers, Solution to Problem 12094 by Roberto Tauraso, ibid., Vol. 127, No. 8 (2020), pp. 755-757.
Programs
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Mathematica
RealDigits[48/Pi - 16*(1 - Log[2]) - 32*Catalan/Pi, 10, 100][[1]]
Formula
Equals 48/Pi - 16*(1 - log(2)) - 32*G/Pi, where G is Catalan's constant (A006752).
Equals 4F3(1/2, 1/2, 1, 1; 2, 2, 2; 1), where pFq() is the generalized hypergeometric function.