A244648 Decimal expansion of the sum of the reciprocals of the hendecagonal numbers (A051682).

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

Offset

1,3

Links

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

Wikipedia, Polygonal number

Formula

Sum_{n=1..infinity} 2/(9n^2 - 7n).

Equals (5*log(3) + Pi*cot(2*Pi/9) - 4*cos(2*Pi/9)*log(cos(Pi/18)) + 4*cos(Pi/9)*log(sin(2*Pi/9)) - 4*log(sin(Pi/9))*sin(Pi/18))/7. - Vaclav Kotesovec, Jul 04 2014

Example

1.195434116529627974352499234698499354884682627084658062386021603017...

Mathematica

RealDigits[ Sum[2/(9n^2 - 7n), {n, 1 , Infinity}], 10, 111][[1]]

Crossrefs

Cf. A000038, A013661, A244639, A244644, A244645, A244646, A244647, A244649.

Sequence in context: A336334 A139604 A104139 * A198359 A071831 A245294

Adjacent sequences: A244645 A244646 A244647 * A244649 A244650 A244651

Keyword

nonn,cons,easy

Author

Robert G. Wilson v, Jul 03 2014

Status

approved