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A283719 Main diagonal of A283674.

%I A283719 #18 Oct 24 2018 02:32:43
%S A283719 1,1,17,19748,4295531890,298024338096736401,
%T A283719 10314425731041362057808006400,
%U A283719 256923578002337121862310634348534055243302,6277101735598269851830651637045695165917698976435202316054
%N A283719 Main diagonal of A283674.
%H A283719 Seiichi Manyama, <a href="/A283719/b283719.txt">Table of n, a(n) for n = 0..26</a>
%F A283719 a(n) ~ n^(n^2) * (1 + 1/(exp(n-1/2)*n^n)). - _Vaclav Kotesovec_, Mar 17 2017
%t A283719 nmax = 20; Table[SeriesCoefficient[Product[1/(1 - x^k)^(k^(n*k)), {k, 1, nmax}], {x, 0, n}], {n, 0, nmax}] (* _Vaclav Kotesovec_, Mar 17 2017 *)
%o A283719 (Ruby)
%o A283719 def s(k, i)
%o A283719   s = 0
%o A283719   (1..i).each{|j| s += j ** (k * j + 1) if i % j == 0}
%o A283719   s
%o A283719 end
%o A283719 def A(k, n)
%o A283719   ary = [1]
%o A283719   s_ary = [0] + (1..n).map{|i| s(k, i)}
%o A283719   (1..n).each{|i| ary << (1..i).inject(0){|s, j| s + ary[-j] * s_ary[j]} / i}
%o A283719   ary
%o A283719 end
%o A283719 def A283719(n)
%o A283719   (0..n).map{|i| A(i, i)[-1]}
%o A283719 end
%Y A283719 Cf. A283674.
%K A283719 nonn
%O A283719 0,3
%A A283719 _Seiichi Manyama_, Mar 15 2017