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a(n) = lcm_{p in Partitions(n)} (Product_{t in p}(t + m)), where m = 2.
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%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