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A281268 Main diagonal of A284993.

%I A281268 #25 Oct 24 2018 02:33:31
%S A281268 1,-1,-3,-20,-54,4935,403432,23308238,-2635805834,-2939783620152,
%T A281268 -1713742918458426,602896713529233651,9901041507182530035347,
%U A281268 52279007840299710266340246,-71905380320280305597098525356,-17521448585729172053338909789657052
%N A281268 Main diagonal of A284993.
%H A281268 Seiichi Manyama, <a href="/A281268/b281268.txt">Table of n, a(n) for n = 0..80</a>
%F A281268 a(n) = [x^n] Product_{k=1..n} 1/(1 + x^k)^(k^n). - _Ilya Gutkovskiy_, Mar 06 2018
%o A281268 (Ruby)
%o A281268 def s(k, n)
%o A281268   s = 0
%o A281268   (1..n).each{|i| s += (-1) ** (n / i + 1) * i ** k if n % i == 0}
%o A281268   s
%o A281268 end
%o A281268 def A(k, n)
%o A281268   ary = [1]
%o A281268   a = [0] + (1..n).map{|i| s(k + 1, i)}
%o A281268   (1..n).each{|i| ary << (1..i).inject(0){|s, j| s - a[j] * ary[-j]} / i}
%o A281268   ary
%o A281268 end
%o A281268 def A281268(n)
%o A281268   (0..n).map{|i| A(i, i)[-1]}
%o A281268 end
%Y A281268 Cf. A284993.
%K A281268 sign
%O A281268 0,3
%A A281268 _Seiichi Manyama_, Apr 13 2017