A283719 Main diagonal of A283674.

1, 1, 17, 19748, 4295531890, 298024338096736401, 10314425731041362057808006400, 256923578002337121862310634348534055243302, 6277101735598269851830651637045695165917698976435202316054

Offset: 0

Author

Seiichi Manyama, Mar 15 2017

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..26

Crossrefs

Cf. A283674.

Programs

Mathematica

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 *)

Ruby

def s(k, i)
  s = 0
  (1..i).each{|j| s += j ** (k * j + 1) if i % j == 0}
  s
end
def A(k, n)
  ary = [1]
  s_ary = [0] + (1..n).map{|i| s(k, i)}
  (1..n).each{|i| ary << (1..i).inject(0){|s, j| s + ary[-j] * s_ary[j]} / i}
  ary
end
def A283719(n)
  (0..n).map{|i| A(i, i)[-1]}
end

Formula

a(n) ~ n^(n^2) * (1 + 1/(exp(n-1/2)*n^n)). - Vaclav Kotesovec, Mar 17 2017