A100443 Inverse binomial transform of A003418.

1, 0, 1, 2, -3, 44, -215, 1014, -3647, 11528, -35919, 135530, -597179, 2850132, -13623623, 60226334, -236639535, 832756304, -2732731487, 9035612658, -33172306739, 138937617020, -615393110199, 2649206536262, -10668440765663, 40078777939224, -142523015012975

Offset: 0

Author

N. J. A. Sloane, Nov 21 2004

Keywords

• sign

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A003418.

Programs

Magma

[(&+[(-1)^(n-k)*Binomial(n,k)*Lcm([1..k]): k in [0..n]]): n in [0..50]]; // G. C. Greubel, Apr 08 2023

Mathematica

A100443[n_]:= (-1)^n +Sum[(-1)^(n-k)*Binomial[n, k]*Apply[LCM, Range[1, k]], {k,n}];
Table[A100443[n], {n,0,50}] (* G. C. Greubel, Apr 08 2023 *)

SageMath

def A100443(n): return sum((-1)^(n-k)*binomial(n,k)*lcm(range(1,k+1)) for k in range(n+1) )
[A100443(n) for n in range(61)] # G. C. Greubel, Apr 08 2023

Formula

a(n) = Sum_{j=0..n} (-1)^(n-j)*binomial(n,j)*A003418(j). - G. C. Greubel, Apr 08 2023