A196554 - OEIS

A196554

Decimal expansion of Sum_{i>=0} 1/((8*i+1)*(8*i+5)).

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

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OFFSET

0,1

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

L. B. W. Jolley, Summation of Series, Dover, 1961, eq. 266 p. 48.

FORMULA

Equals sqrt(2)*(Pi + log(3 + 2^(3/2)))/32.

EXAMPLE

0.21674324683497 = 1/5 + 1/117 + 1/357 + 1/725 + 1/1221 + 1/1845 + ...

MAPLE

sqrt(2)/32*(Pi+log(3+2*sqrt(2))) ; evalf(%) ;

MATHEMATICA

RealDigits[(Sqrt[2]/32)(Pi + Log[3 + 2 Sqrt[2]]), 10, 74][[1]] (* Bruno Berselli, Dec 20 2011 *)

CROSSREFS

Sequence in context: A059364 A258870 A217922 * A244647 A324037 A160348

Adjacent sequences: A196551 A196552 A196553 * A196555 A196556 A196557

KEYWORD

cons,easy,nonn

AUTHOR

R. J. Mathar, Oct 03 2011

STATUS

approved