A100442 Binomial transform of A003418.
1, 2, 5, 16, 53, 206, 757, 2780, 10481, 39898, 146981, 531752, 1939885, 7397846, 29864213, 122842036, 488455217, 1830814610, 6508723141, 22667908448, 81343971941, 312864734302, 1280329420085, 5332923123596, 21687872072113, 84397157118026, 313673593771877
Offset: 1
Keywords
Links
- G. C. Greubel, Table of n, a(n) for n = 1..1000
Programs
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Magma
[(&+[Binomial(n-1,k)*Lcm([1..k]): k in [0..n-1]]): n in [1..50]]; // G. C. Greubel, Apr 08 2023
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Mathematica
A100442[n_]:= 1 +Sum[Binomial[n-1,k]*Apply[LCM, Range[1,k]], {k,n-1}]; Table[A100442[n], {n,50}] (* G. C. Greubel, Apr 08 2023 *)
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SageMath
def A100442(n): return sum(binomial(n-1,k)*lcm(range(1,k+1)) for k in range(n) ) [A100442(n) for n in range(1,51)] # G. C. Greubel, Apr 08 2023
Formula
a(n) = Sum_{j=0..n-1} binomial(n-1,j)*A003418(j). - G. C. Greubel, Apr 08 2023