A228045 Decimal expansion of sum of reciprocals of row 3 of the natural number array, A185787.

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

Offset

0,1

Comments

See A228044.

Links

Table of n, a(n) for n=0..85.

Formula

Equals 1/6 + 1/9 + 1/13 + ...

Equals (1/276)*(-161 + 48*r*tanh(r)), where r = (Pi/2)*sqrt(23).

Example

0.726800619464935778179143007194435...

Mathematica

$MaxExtraPrecision = Infinity; t[n_, k_] := t[n, k] = n + (n + k - 2) (n + k - 1)/2; u = N[Sum[1/t[3, k], {k, 1, Infinity}], 130]; RealDigits[u, 10]

Crossrefs

Cf. A185787, A000027, A228044, A226985.

Sequence in context: A322933 A143306 A199075 * A011361 A199433 A095398

Adjacent sequences: A228042 A228043 A228044 * A228046 A228047 A228048

Keyword

nonn,cons,easy

Author

Clark Kimberling, Aug 06 2013

Status

approved