A075136 - OEIS

%I #9 Dec 15 2014 04:30:50

%S 1,6,59,812,14389,104038,534113,15837352,177575597,6681333014,

%T 278042982799,93928709068,665521987201,35665695484178,684591747070657,

%U 42155877944972752,42527303541794647,986175536059084606

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

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

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

%F Sum 1/a(n) = 1.111939597509272224249... - _Cino Hilliard_, Dec 21 2003

%t a=4; b=1; maxN=20; s=0; Numerator[Table[s+=1/(a n + b), {n, 0, maxN-1}]]

%t Numerator[Accumulate[1/Range[1,69,4]]] (* _Harvey P. Dale_, Dec 15 2014 *)

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

%Y Cf. A051539, A075135.

%K easy,frac,nonn

%O 1,2

%A _T. D. Noe_, Sep 04 2002