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

1,3

Links

Table of n, a(n) for n=1..105.

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.

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.

Example

1.03928049679487622006025262010356644086601121330111...

Mathematica

RealDigits[48/Pi - 16*(1 - Log[2]) - 32*Catalan/Pi, 10, 100][[1]]

Crossrefs

Cf. A000984, A006752, A143233, A244009.

Sequence in context: A293383 A094724 A008564 * A354129 A060956 A125301

Adjacent sequences: A348368 A348369 A348370 * A348372 A348373 A348374

Keyword

nonn,cons

Author

Amiram Eldar, Oct 15 2021

Status

approved