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

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Formula

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

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 *)

Prog

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

Crossrefs

Cf. A003418, A100443.

Sequence in context: A148397 A148398 A346518 * A081126 A018191 A006191

Adjacent sequences: A100439 A100440 A100441 * A100443 A100444 A100445

Keyword

nonn

Author

N. J. A. Sloane, Nov 21 2004

Status

approved