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%I #9 Dec 14 2023 16:28:33
%S 1,1,1,1,2,2,1,3,12,6,1,1,9,24,12,1,5,5,135,720,60,1,1,25,5,405,1440,
%T 360,1,7,7,875,175,8505,60480,2520,1,1,49,7,4375,175,127575,120960,
%U 5040,1,1,1,343,49,21875,875,382725,3628800,15120
%N Cumulative products of the generalized Clausen numbers. Array read by ascending antidiagonals.
%C A160014 are the generalized Clausen numbers, for m = 0 the formula computes the cumulative radical A048803, and for m = 1 the Hirzebruch numbers A091137.
%F A(m, n) = A160014(m, n) * A(m, n - 1) for n > 0 and A(m, 0) = 1.
%e Array A(m, n) starts:
%e [0] 1, 1, 2, 6, 12, 60, 360, 2520, ... A048803
%e [1] 1, 2, 12, 24, 720, 1440, 60480, 120960, ... A091137
%e [2] 1, 3, 9, 135, 405, 8505, 127575, 382725, ... A368092
%e [3] 1, 1, 5, 5, 175, 175, 875, 875, ...
%e [4] 1, 5, 25, 875, 4375, 21875, 765625, 42109375, ...
%e [5] 1, 1, 7, 7, 49, 49, 3773, 3773, ...
%e [6] 1, 7, 49, 343, 2401, 184877, 1294139, 117766649, ...
%e [7] 1, 1, 1, 1, 11, 11, 143, 143, ...
%e [8] 1, 1, 1, 11, 11, 143, 1573, 1573, ...
%e [9] 1, 1, 11, 11, 1573, 1573, 17303, 17303, ...
%o (SageMath)
%o from functools import cache
%o def Clausen(n, k):
%o return mul(s for s in map(lambda i: i+n, divisors(k)) if is_prime(s))
%o @cache
%o def CumProdClausen(m, n):
%o return Clausen(m, n) * CumProdClausen(m, n - 1) if n > 0 else 1
%o for m in range(10): print([m], [CumProdClausen(m, n) for n in range(8)])
%Y Cf. A160014, A048803 (m=0), A091137 (m=1), A368092 (m=2).
%Y Cf. A171080, A238963, A368116, A368048.
%K nonn,tabl
%O 0,5
%A _Peter Luschny_, Dec 12 2023
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