A075136 Numerator of the generalized harmonic number H(n,4,1).

1, 6, 59, 812, 14389, 104038, 534113, 15837352, 177575597, 6681333014, 278042982799, 93928709068, 665521987201, 35665695484178, 684591747070657, 42155877944972752, 42527303541794647, 986175536059084606

Offset: 1

Author

T. D. Noe, Sep 04 2002

Keywords

• easy
• frac
• nonn

Comments

The denominators are in A051539. See A075135 for more details.

Numerators of the partial sums of the divergent series 1/3 + 1/7 + 1/11 + . . 1/(4n-1).

Crossrefs

Cf. A051539, A075135.

Programs

Mathematica

a=4; b=1; maxN=20; s=0; Numerator[Table[s+=1/(a n + b), {n, 0, maxN-1}]]
Numerator[Accumulate[1/Range[1,69,4]]] (* Harvey P. Dale, Dec 15 2014 *)

PARI

sumrecip(n,a,b) = { s=0; default(realprecision,n); forstep(j=b,n,a, s=s+1/j; print1(numerator(s)",") ) }

Formula

Sum 1/a(n) = 1.111939597509272224249... - Cino Hilliard, Dec 21 2003