A074199 a(n) = n!/(1!*2!*3!*...*k!) where k is the largest integer such that 1!*2!*3!*...*k! divides n!.

1, 1, 3, 2, 10, 60, 420, 140, 1260, 105, 1155, 13860, 180180, 2522520, 37837800, 840840, 14294280, 51051, 969969, 19399380, 407386980, 8962513560, 206137811880, 4947307485120, 123682687128000, 79755701025, 2153403927675, 60295309974900, 1748563989272100, 52456919678163000

Offset

1,3

Links

Amiram Eldar, Table of n, a(n) for n = 1..747

Formula

a(n) = n!/A000178(A074198(n)). - Amiram Eldar, May 14 2024

Mathematica

a[n_] := Module[{k = 1}, NestWhile[# / (++k)! &, n!, IntegerQ] * k!]; Array[a, 30] (* Amiram Eldar, May 14 2024 *)

Prog

(PARI) a(n)=n!/prod(i=1, if(n<0, 0, s=1; while(n!%prod(i=1, s, i!)==0, s++); s-1), i!)

Crossrefs

Cf. A000178, A074198.

Similar to but different from A088302.

Sequence in context: A335719 A096073 A088302 * A153187 A248242 A215598

Adjacent sequences: A074196 A074197 A074198 * A074200 A074201 A074202

Keyword

easy,nonn

Author

Benoit Cloitre, Sep 17 2002

Extensions

More terms from Amiram Eldar, May 14 2024

Status

approved