A074637 Numerator of 4 * H(n,4,3), a generalized harmonic number.

4, 40, 524, 976, 20084, 491192, 13935164, 450160544, 93250876, 1249813672, 55206526972, 2657681947952, 46167204272716, 235410309457592, 14140794103168588, 14376406243883968, 978062783205294796

Offset: 1

Author

Robert G. Wilson v, Aug 27 2002

Keywords

• easy
• frac
• nonn

Crossrefs

The denominators are in A074638.

Cf. A075135.

Programs

Mathematica

Table[ Numerator[ Sum[1/i, {i, 3/4, n}]], {n, 1, 20}]

Formula

a(n) = numerator(4 * Sum_{j=0..n-1} 1/(4*j + 3)) = numerator(Psi(n + 3/4) - Psi(3/4)), with the Digamma function Psi(z). See a comment in A074638 with the Abramowitz-Stegun link. - Wolfdieter Lang, Apr 05 2022

Extensions

Better description from T. D. Noe, Sep 04 2002