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Binomial transform of A003418.
1

%I #9 Apr 08 2023 02:28:56

%S 1,2,5,16,53,206,757,2780,10481,39898,146981,531752,1939885,7397846,

%T 29864213,122842036,488455217,1830814610,6508723141,22667908448,

%U 81343971941,312864734302,1280329420085,5332923123596,21687872072113,84397157118026,313673593771877

%N Binomial transform of A003418.

%H G. C. Greubel, <a href="/A100442/b100442.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = Sum_{j=0..n-1} binomial(n-1,j)*A003418(j). - _G. C. Greubel_, Apr 08 2023

%t A100442[n_]:= 1 +Sum[Binomial[n-1,k]*Apply[LCM, Range[1,k]], {k,n-1}];

%t Table[A100442[n], {n,50}] (* _G. C. Greubel_, Apr 08 2023 *)

%o (Magma) [(&+[Binomial(n-1,k)*Lcm([1..k]): k in [0..n-1]]): n in [1..50]]; // _G. C. Greubel_, Apr 08 2023

%o (SageMath)

%o def A100442(n): return sum(binomial(n-1,k)*lcm(range(1,k+1)) for k in range(n) )

%o [A100442(n) for n in range(1,51)] # _G. C. Greubel_, Apr 08 2023

%Y Cf. A003418, A100443.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Nov 21 2004