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a(n) = Sum_{d|n} (-1)^(n/d-1) * binomial(d+3,4).
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%I #13 Oct 25 2023 18:20:51

%S 1,4,16,29,71,115,211,289,511,649,1002,1253,1821,2174,3146,3505,4846,

%T 5605,7316,8099,10852,11653,14951,16333,20546,21935,27916,28904,35961,

%U 38620,46377,48113,59922,61204,74096,77024,91391,93959,113766,114059,135752,140654,163186

%N a(n) = Sum_{d|n} (-1)^(n/d-1) * binomial(d+3,4).

%H Michael De Vlieger, <a href="/A366814/b366814.txt">Table of n, a(n) for n = 1..10000</a>

%F G.f.: -Sum_{k>=1} (-x)^k/(1-x^k)^5 = Sum_{k>=1} binomial(k+3,4) * x^k/(1+x^k).

%t Table[DivisorSum[n, (-1)^(n/# - 1)*Binomial[# + 3, 4] &], {n, 56}] (* _Michael De Vlieger_, Oct 25 2023 *)

%o (PARI) a(n) = sumdiv(n, d, (-1)^(n/d-1)*binomial(d+3, 4));

%Y Partial sums give A366723.

%Y Cf. A000593, A365007, A366813.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Oct 24 2023