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A366659 a(n) = Sum_{k=1..n} (-1)^(k-1) * binomial(floor(n/k)+3,4).

%I A366659 #26 Oct 26 2023 08:32:25
%S A366659 1,4,15,30,66,115,200,295,471,659,946,1259,1715,2194,2920,3591,4561,
%T A366659 5585,6916,8216,10082,11823,14124,16389,19350,22174,26004,29435,33931,
%U A366659 38445,43902,48925,55767,61941,69831,77275,86415,94968,106094,115874,128216,140214,154405
%N A366659 a(n) = Sum_{k=1..n} (-1)^(k-1) * binomial(floor(n/k)+3,4).
%H A366659 Michael De Vlieger, <a href="/A366659/b366659.txt">Table of n, a(n) for n = 1..10000</a>
%F A366659 a(n) = Sum_{k=1..n} binomial(k+2,3) * (floor(n/k) mod 2).
%F A366659 G.f.: -1/(1-x) * Sum_{k>=1} (-x)^k/(1-x^k)^4 = 1/(1-x) * Sum_{k>=1} binomial(k+2,3) * x^k/(1+x^k).
%t A366659 Array[Sum[(-1)^(k - 1)*Binomial[Floor[#/k] + 3, 4], {k, #}] &, 56] (* _Michael De Vlieger_, Oct 25 2023 *)
%o A366659 (PARI) a(n) = sum(k=1, n, (-1)^(k-1)*binomial(n\k+3, 4));
%Y A366659 Partial sums of A366813.
%Y A366659 Cf. A078471, A366395, A366723.
%K A366659 nonn
%O A366659 1,2
%A A366659 _Seiichi Manyama_, Oct 24 2023