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a(n) = n!/(1!*2!*3!*...*k!) where k is the largest integer such that 1!*2!*3!*...*k! divides n!.
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%I #15 May 14 2024 03:59:14

%S 1,1,3,2,10,60,420,140,1260,105,1155,13860,180180,2522520,37837800,

%T 840840,14294280,51051,969969,19399380,407386980,8962513560,

%U 206137811880,4947307485120,123682687128000,79755701025,2153403927675,60295309974900,1748563989272100,52456919678163000

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

%H Amiram Eldar, <a href="/A074199/b074199.txt">Table of n, a(n) for n = 1..747</a>

%F a(n) = n!/A000178(A074198(n)). - _Amiram Eldar_, May 14 2024

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

%o (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!)

%Y Cf. A000178, A074198.

%Y Similar to but different from A088302.

%K easy,nonn

%O 1,3

%A _Benoit Cloitre_, Sep 17 2002

%E More terms from _Amiram Eldar_, May 14 2024