A080474 - OEIS

A080474

a(n) = product of sum of taking n-1 numbers from the next n numbers. The next n numbers can be grouped like this (1), (2,3), (4,5,6), (7,8,9,10),... . Let N be the sum of all the members of the n-th group. Let k be a member and f(k) = N - k. Then a(n) = the product of all f(k) for k taking all member values.

%I #9 Sep 21 2025 17:16:59

%S 1,6,990,421200,379501200,625757605200,1707530790369600,

%T 7172573016426048000,43928207579534870592000,

%U 376055676152225153019936000,4350748615258091511751558272000

%N a(n) = product of sum of taking n-1 numbers from the next n numbers. The next n numbers can be grouped like this (1), (2,3), (4,5,6), (7,8,9,10),... . Let N be the sum of all the members of the n-th group. Let k be a member and f(k) = N - k. Then a(n) = the product of all f(k) for k taking all member values.

%H Harvey P. Dale, <a href="/A080474/b080474.txt">Table of n, a(n) for n = 1..158</a>

%e a(3)= 990. The third group of next n numbers is (4,5,6) and a(3) = (4+5)*(5+6)*(4+6)= 990.

%t Join[{1},Rest[Times@@(Total/@Subsets[#,{Length[#]-1}])&/@Module[{nn=12,tl},tl=TakeList[Range[(nn(nn+1))/2],Range[nn]];tl]]] (* _Harvey P. Dale_, Jul 21 2025 *)

%Y Cf. A080473.

%K nonn

%O 1,2

%A _Amarnath Murthy_, Mar 11 2003

%E More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 06 2003