%I #44 Mar 19 2024 13:47:54
%S 1,1,2,6,12,420,10920,13791960,31781240978760,
%T 2475081972959523523910954640,
%U 3442004402022863055515137969749021701676249608093520,45446117889526225044218072480163823127876682090382722344419488836545177458721523373548206735891390800
%N a(0) = 1; for n > 0, a(n) = lcm(a(n-1), a(n-2)+1, a(n-3)+2, ..., a(0)+n-1).
%F a(n) = lcm_{k=0..n-1} a(n-1 - k) + k with a(0)=1.
%e Prepend a(n-1)
%e after incrementing the value
%e in each of these columns
%e | | | |
%e v v v v
%e n=0: 1 = a(0),
%e n=1: lcm( a(0) ) = lcm( 1) = 1 = a(1),
%e n=2: lcm( a(1), a(0)+1) = lcm( 1,2) = 2 = a(2),
%e n=3: lcm( a(2), a(1)+1, a(0)+2) = lcm( 2,2,3) = 6 = a(3),
%e n=4: lcm(a(3), a(2)+1, a(1)+2, a(0)+3) = lcm(6,3,3,4) = 12 = a(4).
%o (Python)
%o import math
%o def a(n):
%o p=[1]
%o for i in range(n):
%o p.append(math.lcm(*p))
%o for x in range(0, len(p)-1):
%o p[x]+=1
%o return p[-1]
%K nonn
%O 0,3
%A _Justin Dugan_, Nov 13 2023