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%I #7 Apr 08 2023 02:28:42
%S 1,0,1,2,-3,44,-215,1014,-3647,11528,-35919,135530,-597179,2850132,
%T -13623623,60226334,-236639535,832756304,-2732731487,9035612658,
%U -33172306739,138937617020,-615393110199,2649206536262,-10668440765663,40078777939224,-142523015012975
%N Inverse binomial transform of A003418.
%H G. C. Greubel, <a href="/A100443/b100443.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) = Sum_{j=0..n} (-1)^(n-j)*binomial(n,j)*A003418(j). - _G. C. Greubel_, Apr 08 2023
%t A100443[n_]:= (-1)^n +Sum[(-1)^(n-k)*Binomial[n, k]*Apply[LCM, Range[1, k]], {k,n}];
%t Table[A100443[n], {n,0,50}] (* _G. C. Greubel_, Apr 08 2023 *)
%o (Magma) [(&+[(-1)^(n-k)*Binomial(n,k)*Lcm([1..k]): k in [0..n]]): n in [0..50]]; // _G. C. Greubel_, Apr 08 2023
%o (SageMath)
%o def A100443(n): return sum((-1)^(n-k)*binomial(n,k)*lcm(range(1,k+1)) for k in range(n+1) )
%o [A100443(n) for n in range(61)] # _G. C. Greubel_, Apr 08 2023
%Y Cf. A003418.
%K sign
%O 0,4
%A _N. J. A. Sloane_, Nov 21 2004
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