A228047 Decimal expansion of sum of reciprocals of row 5 of the natural number array, A185787.

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

Offset: 0

Author

Clark Kimberling, Aug 06 2013

Keywords

• nonn
• cons
• easy

Comments

See A228044.

Examples

			0.42353909960870019683760768997442893...
		

Crossrefs

Cf. A185787, A000027, A228044, A226985.

Programs

Mathematica

$MaxExtraPrecision = Infinity; t[n_, k_] := t[n, k] = n + (n + k - 2) (n + k - 1)/2; u = N[Sum[1/t[5, k], {k, 1, Infinity}], 130]; RealDigits[u, 10]

PARI

sumnumrat(1/(n*(n+7)/2+11),1) \\ Charles R Greathouse IV, Feb 08 2023

Formula

Equals 1/15 + 1/20 + 1/26 + ...

Equals (1/17160)*(-9997 + 1760*r*tanh(r)), where r = (Pi/2)*sqrt(39).