%I #17 Nov 27 2024 16:00:58
%S 1,-1,0,-2,0,-2,0,-2,0,-5,1,-2,1,-2,0,-14,0,-2,1,-2,0,-18,0,-2,0,-7,1,
%T -23,0,-2,6,-2,0,-26,1,-26,4,-2,0,-30,0,-2,6,-2,1,-286,0,-2,0,-9,7,
%U -38,0,-2,8,-38,1,-42,1,-2,7,-2,0,-493,0,-44,9,-2,0,-50,10,-2,0,-2,1,-698,1,-50,12,-2,0,-239,1,-2,10,-56
%N a(n) = [x^n] Product_{d|n} 1/(1 + x^d).
%H Antti Karttunen, <a href="/A300548/b300548.txt">Table of n, a(n) for n = 0..10201</a>
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F a(n) = -2 if n is an odd prime (A065091).
%t Table[SeriesCoefficient[Product[1/(1 + Boole[Mod[n, k] == 0] x^k), {k, 1, n}], {x, 0, n}], {n, 0, 85}]
%o (PARI) A300548(n) = if(!n, 1, my(p=1); fordiv(n, d, p /= (1 + 'x^d)); polcoeff(Ser(p, 'x, 1+n), n)); \\ _Antti Karttunen_, Nov 27 2024
%Y Cf. A018818, A033630, A065091, A081362, A300547, A300549.
%K sign
%O 0,4
%A _Ilya Gutkovskiy_, Mar 08 2018