cp's OEIS Frontend

A366985 a(n) = Sum_{k=1..n} binomial(k+3,3) * floor(n/k).

%I A366985 #13 Oct 31 2023 09:47:04
%S A366985 4,18,42,91,151,269,393,607,851,1207,1575,2183,2747,3561,4457,5640,
%T A366985 6784,8452,9996,12158,14326,17004,19608,23306,26642,30870,35174,40518,
%U A366985 45482,52214,58202,65930,73458,82382,90998,102295,112179,124393,136457,151125,164373
%N A366985 a(n) = Sum_{k=1..n} binomial(k+3,3) * floor(n/k).
%F A366985 G.f.: 1/(1-x) * Sum_{k>0} (1/(1-x^k)^4 - 1) = 1/(1-x) * Sum_{k>0} binomial(k+3,3) * x^k/(1-x^k).
%o A366985 (PARI) a(n) = sum(k=1, n, binomial(k+3, 3)*(n\k));
%o A366985 (Python)
%o A366985 from math import isqrt
%o A366985 def A366985(n): return (-(s:=isqrt(n))*(s*(s*(s*(s+11)+45)+85)+74)+sum(((q:=n//w)+1)*(q*(q*(q+9)+26)+((w+4)*(w*(w+2)+3)<<2)) for w in range(1,s+1)))//3>>3 # _Chai Wah Wu_, Oct 31 2023
%Y A366985 Partial sums of A116963.
%Y A366985 Cf. A006218, A366983, A366984.
%Y A366985 Cf. A366971.
%K A366985 nonn
%O A366985 1,1
%A A366985 _Seiichi Manyama_, Oct 30 2023