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%I #8 Aug 23 2019 14:09:34
%S 1,3,10,53,266,2093,14512,134705,1317724,14339429,156052942,
%T 2243410945,28893239818,421448538895,6810085942104,117497037128065,
%U 1980909279322608,38790292385240321,730946685781179418,15916872348230275385,346942995035062132634,7767365425379382284307
%N a(n) = Sum_{k=1..n} (-1)^(n-k) * Stirling1(n,k) * floor(n/k).
%F a(n) = [x^n] (1/(1 - x)) * Sum_{k=1..n} (-1)^(n-k) * Stirling1(n,k) * x^k/(1 - x^k).
%F a(n) = Sum_{k=1..n} Sum_{d|k} (-1)^(n-d) * Stirling1(n,d).
%t Table[Sum[(-1)^(n - k) StirlingS1[n, k] Floor[n/k] , {k, 1, n}], {n, 1, 22}]
%t Table[SeriesCoefficient[1/(1 - x) Sum[(-1)^(n - k) StirlingS1[n, k] x^k/(1 - x^k), {k, 1, n}], {x, 0, n}], {n, 1, 22}]
%t Table[Sum[Sum[(-1)^(n - d) StirlingS1[n, d], {d, Divisors[k]}], {k, 1, n}], {n, 1, 22}]
%o (PARI) a(n) = sum(k=1, n, (-1)^(n-k)*stirling(n, k, 1) * (n\k)); \\ _Michel Marcus_, Aug 23 2019
%Y Cf. A008275, A096308, A308812, A309911.
%K nonn
%O 1,2
%A _Ilya Gutkovskiy_, Aug 22 2019
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