%I #11 Dec 17 2023 18:27:50
%S 1,3,36,540,6480,136080,8164800,24494400,293932800,48498912000,
%T 4073908608000,158882435712000,9532946142720000,28598838428160000,
%U 343186061137920000,612587119131187200000,7351045429574246400000,419009589485732044800000,276546329060583149568000000
%N a(n) = lcm_{p in Partitions(n)} (Product_{t in p}(t + m)), where m = 2.
%C With m = 0, the cumulative radical A048803 is computed, and with m = 1 the Hirzebruch numbers A091137. The general array is A368116. Using the terminology introduced in A368116 a(n) = lcm_{p in P_{2}(n)} Prod(p).
%F a(n) = A368092(n) * 2^(n - n mod 2).
%e Let n = 4. The partitions of 4 are [(4), (3, 1), (2, 2), (2, 1, 1), (1, 1, 1, 1)]. Thus a(4) = lcm([6, 5*3, 4*4, 4*3*3, 3*3*3*3]) = 6480.
%o (SageMath)
%o def a(n): return lcm(product(r + 2 for r in p) for p in Partitions(n))
%o print([a(n) for n in range(20)])
%Y Cf. A368092, A048803, A091137, A368116.
%K nonn
%O 0,2
%A _Peter Luschny_, Dec 12 2023