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A283720 Main diagonal of A283675.

%I A283720 #15 Oct 24 2018 02:32:46
%S A283720 1,-1,-16,-19619,-4294403215,-298022109672568357,
%T A283720 -10314423865939993706950978963,
%U A283720 -256923577039780637227768848162543179896514,-6277101735175091675863380669683250419973895230549186236030
%N A283720 Main diagonal of A283675.
%H A283720 Seiichi Manyama, <a href="/A283720/b283720.txt">Table of n, a(n) for n = 0..26</a>
%t A283720 Table[SeriesCoefficient[Product[(1 - x^k)^(k^(n*k)), {k, 1, 10}], {x, 0, n}], {n, 0, 10}] (* _Indranil Ghosh_, Mar 17 2017 *)
%o A283720 (Ruby)
%o A283720 def s(k, i)
%o A283720   s = 0
%o A283720   (1..i).each{|j| s += j ** (k * j + 1) if i % j == 0}
%o A283720   s
%o A283720 end
%o A283720 def A(k, n)
%o A283720   ary = [1]
%o A283720   s_ary = [0] + (1..n).map{|i| s(k, i)}
%o A283720   (1..n).each{|i| ary << (1..i).inject(0){|s, j| s - ary[-j] * s_ary[j]} / i}
%o A283720   ary
%o A283720 end
%o A283720 def A283720(n)
%o A283720   (0..n).map{|i| A(i, i)[-1]}
%o A283720 end
%Y A283720 Cf. A283675.
%K A283720 sign
%O A283720 0,3
%A A283720 _Seiichi Manyama_, Mar 15 2017