A283719 - OEIS

%I #18 Oct 24 2018 02:32:43

%S 1,1,17,19748,4295531890,298024338096736401,

%T 10314425731041362057808006400,

%U 256923578002337121862310634348534055243302,6277101735598269851830651637045695165917698976435202316054

%N Main diagonal of A283674.

%H Seiichi Manyama, <a href="/A283719/b283719.txt">Table of n, a(n) for n = 0..26</a>

%F a(n) ~ n^(n^2) * (1 + 1/(exp(n-1/2)*n^n)). - _Vaclav Kotesovec_, Mar 17 2017

%t 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 (Ruby)

%o def s(k, i)

%o   s = 0

%o   (1..i).each{|j| s += j ** (k * j + 1) if i % j == 0}

%o   s

%o end

%o def A(k, n)

%o   ary = [1]

%o   s_ary = [0] + (1..n).map{|i| s(k, i)}

%o   (1..n).each{|i| ary << (1..i).inject(0){|s, j| s + ary[-j] * s_ary[j]} / i}

%o   ary

%o end

%o def A283719(n)

%o   (0..n).map{|i| A(i, i)[-1]}

%o end

%Y Cf. A283674.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Mar 15 2017