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%I #5 Feb 01 2018 20:57:16
%S 1,-1,0,15,-136,885,-4896,43085,-787200,7775271,326355200,
%T -22138191801,781498160640,-18924340012435,239123351330304,
%U 5915023788331125,-568462201562300416,25327272129182225295,-795994018378027868160,15538852668590468027711
%N a(n) = n! * [x^n] Product_{k>=1} (1 - x^k)^(n/k).
%F a(n) = n! * [x^n] exp(-n*Sum_{k>=1} d(k)*x^k/k), where d(k) is the number of divisors of k (A000005).
%e The table of coefficients of x^k in expansion of e.g.f. Product_{k>=1} (1 - x^k)^(n/k) begins:
%e n = 0: (1), 0, 0, 0, 0, 0, 0, ...
%e n = 1: 1, (-1), -1, 1, -1, 41, -131, ...
%e n = 2: 1, -2, (0), 8, -4, 72, -704, ...
%e n = 3: 1, -3, 3, (15), -45, 63, -1539, ...
%e n = 4: 1, -4, 8, 16, (-136), 224, -1856, ...
%e n = 5: 1, -5, 15, 5, -265, (885), -2075, ...
%e n = 6: 1, -6, 24, -24, -396, 2376, (-4896), ...
%t Table[n! SeriesCoefficient[Product[(1 - x^k)^(n/k), {k, 1, n}], {x, 0, n}], {n, 0, 19}]
%Y Cf. A000005, A028343, A281267, A299034.
%K sign
%O 0,4
%A _Ilya Gutkovskiy_, Feb 01 2018