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A368092 a(n) = A160014(m, n) * a(n - 1) for m = 2 and n > 0, a(0) = 1.

%I A368092 #9 Dec 14 2023 16:28:41
%S A368092 1,3,9,135,405,8505,127575,382725,1148175,189448875,3978426375,
%T A368092 155158628625,2327379429375,6982138288125,20946414864375,
%U A368092 37389350532909375,112168051598728125,6393578941127503125,1054940525286038015625,3164821575858114046875,66461253093020394984375
%N A368092 a(n) = A160014(m, n) * a(n - 1) for m = 2 and n > 0, a(0) = 1.
%C A368092 A160014 are the generalized Clausen numbers. For m = 0 the formula computes the cumulative radical A048803, for m = 1 the Hirzebruch numbers A091137.
%F A368092 a(n) = 2^(n mod 2 - n)*lcm_{p in Partitions(n)} (Product_{t in p}(t + 2)).
%F A368092 a(n) = 2^(n mod 2 - n)*A368048(n).
%F A368092 a(n) = A368117(n) * a(n-1) for n > 0.
%o A368092 (SageMath)
%o A368092 from functools import cache
%o A368092 @cache
%o A368092 def a_rec(n):
%o A368092     if n == 0: return 1
%o A368092     p = mul(s for s in map(lambda i: i + 2, divisors(n)) if is_prime(s))
%o A368092     return p * a_rec(n - 1)
%o A368092 print([a_rec(n) for n in range(21)])
%o A368092 # Alternatively, but less efficient:
%o A368092 def a(n): return (2**(n%2 - n) * lcm(product(r + 2 for r in p) for p in Partitions(n)))
%Y A368092 Cf. A160014, A048803 (m=0), A091137 (m=1), this sequence (m=2), A368093 (array), A368048, A368117.
%K A368092 nonn
%O A368092 0,2
%A A368092 _Peter Luschny_, Dec 12 2023