A271563 Decimal expansion of Sum_{j>=0} Sum_{i>=0} (-1/4)^i*(-1)^j*binomial(2i,i)/((2j+1)(i+2j+2)).

3, 4, 4, 5, 4, 3, 6, 3, 6, 7, 9, 2, 3, 7, 0, 6, 4, 0, 3, 3, 2, 0, 5, 3, 3, 8, 7, 9, 0, 0, 2, 0, 4, 3, 0, 6, 5, 8, 9, 4, 2, 5, 9, 7, 4, 6, 1, 3, 5, 9, 2, 1, 2, 5, 5, 0, 8, 5, 7, 7, 7, 9, 6, 3, 2, 8, 5, 7, 8, 3, 4, 4, 2, 8, 6, 2, 5, 2, 7, 6, 2, 1, 0, 4, 5

Offset: 0

Author

John M. Campbell, Apr 09 2016

Keywords

• cons
• nonn

Examples

			0.3445436367923706403320533879002043065894259746135921255085777...
		

Crossrefs

Decimal expansions of hypergeometric series: A244844, A263353, A263354, A263490, A263491, A263492, A263493, A263494, A263495, A263496, A263497, A263498, A229837, A268813, A086731, A002117, A076788.

Programs

Maple

evalf((Pi - 2*sqrt(1+sqrt(2)) * arctan(2*sqrt(2+10*sqrt(2))/7)) / sqrt(2), 120); # Vaclav Kotesovec, Apr 10 2016

Mathematica

RealDigits[(Pi - 2*Sqrt[1 + Sqrt[2]] * ArcTan[(2/7)*Sqrt[2 + 10*Sqrt[2]]])/Sqrt[2], 10, 120][[1]]
N[Sum[Sum[((-1)^(i + j) 4^-i Binomial[2 i, i])/((1 + 2 j) (2 + i + 2 j)), {i, 0, Infinity}], {j, 0, Infinity}]]

PARI

(Pi - 2*sqrt(1+sqrt(2)) * atan(2*sqrt(2+10*sqrt(2))/7)) / sqrt(2)

Formula

Equals (Pi - 2*sqrt(1+sqrt(2)) * arctan(2*sqrt(2+10*sqrt(2))/7)) / sqrt(2). - Vaclav Kotesovec, Apr 10 2016