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%I #28 Aug 25 2017 23:34:21
%S 1,1,1,2,6,12,30,78,186,414,912,2064,4338,9798,20106,40974,80196,
%T 158322,309414,615558,1212402,2417136,4776654,9497508,18726708,
%U 37056150,72946116,144230640,284660874,564451830,1118803818,2224792026,4420041210,8791590168
%N Number of permutations s_1,s_2,...,s_n of 1,2,...,n with s_n = n (if n>0) and such that for all j=1,2,...,n, Sum_{i=1..j} s_i divides Sum_{i=1..j} s_i^3.
%F a(n+1) = A291445(n).
%F A291445(n) >= a(n) + A291519(n) for n > 1.
%e 1 divides 1^3,
%e 1 + 2 divides 1^3 + 2^3,
%e 1 + 2 + 3 divides 1^3 + 2^3 + 3^3,
%e 1 + 2 + 3 + 4 divides 1^3 + 2^3 + 3^3 + 4^3,
%e 1 + 2 + 3 + 4 + 5 divides 1^3 + 2^3 + 3^3 + 4^3 + 5^3.
%e So [1, 2, 3, 4, 5] satisfies all the conditions.
%e -------------------------------------------------------
%e a(1) = 1: [[1]];
%e a(2) = 1: [[1, 2]];
%e a(3) = 2: [[1, 2, 3], [2, 1, 3]];
%e a(4) = 6: [[1, 2, 3, 4], [1, 3, 2, 4], [2, 1, 3, 4], [2, 3, 1, 4], [3, 1, 2, 4], [3, 2, 1, 4]];
%e a(5) = 12: [[1, 2, 3, 4, 5], [1, 3, 2, 4, 5], [2, 1, 3, 4, 5], [2, 3, 1, 4, 5], [2, 3, 4, 1, 5], [2, 4, 3, 1, 5], [3, 1, 2, 4, 5], [3, 2, 1, 4, 5], [3, 2, 4, 1, 5], [3, 4, 2, 1, 5], [4, 2, 3, 1, 5], [4, 3, 2, 1, 5]].
%Y Cf. A291445, A291519.
%K nonn
%O 0,4
%A _Seiichi Manyama_, Aug 25 2017
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