1,2

Decimal expansion is A131915.

Mark B. Villarino, Ramanujan's Harmonic Number Expansion into Negative Powers of a Triangular Number. Constant occurs in Theorem 6, formula (1.13), page 6.

Martin Fuller corrected a typo in the cited paper. It should be: ((12 * gamma) - 11 + (12 * ln(2^0.5))) / (1 - gamma - ln(2^0.5)) or more simply: 1 / (1 - gamma - ln(2^0.5)) - 12.

1.1215093407... = 1 + 1/8+ 1/4+ 1/2+ 1/1+ 1/5+ 1/1+ 1/1+ 1/5+ 1/1+ 1/1+ 1/3+ 1/8+ 1/1+ 1/4+ 1/2+ 1/6+ 1/9+ 1/5+ 1/97+ 1/2+ 1/1+ 1/1+ 1/2+ 1/9+ 1/8+ 1/5+ 1/3+ 1/16+ 1/1+ 1/31+ 1/2+ 1/1+ 1/8+ 1/7+ 1/1+ 1/2+ 1/1+ 1/15+ 1/1+ 1/1+ 1/1+ 1/3+ 1/1+ 1/12+ 1/3+ 1/11+ 1/2+ 1/1+ 1/1+ 1/13+ 1/1+ 1/3+ 1/6+ 1/1+ 1/15+ 1/9+ 1/3+ 1/4+ 1/1+ 1/2+ 1/1+ 1/5+ 1/1+ 1/1+ 1/1+ 1/18+ 1/2+ 1/5+ 1/8+ 1/1+ 1/3+ 1/1+ 1/1+ 1/2+ 1/3+ 1/12+ 1/1+ 1/8+ 1/1+ 1/2+ 1/1+ 1/1+ 1/1+ 1/2+ 1/17+ 1/13+ 1/3+ 1/1+ 1/1+ 1/1+ 1/5+ 1/1+ 1/1+ 1/3+ 1/2+ 1/1+ 1/2+ 1/3+ 1/5+ . . .

Cf. A001008, A001620, A131915, A131917, A131918.

Sequence in context: A145435 A133839 A080828 this_sequence A131606 A033328 A097529

Adjacent sequences: A131913 A131914 A131915 this_sequence A131917 A131918 A131919

cofr,easy,nonn

Jonathan Vos Post (jvospost3(AT)gmail.com), Jul 27 2007