A395075 G.f. A(x) satisfies [x^n] exp( -n*A(x) ) / (1-n^3*x)^(1/n^2) = 0, for n >= 1.

1, 4, 243, 67104, 50280485, 80604257403, 238578075027474, 1178741837443132376, 9036272428220471876577, 101713755052019659176399705, 1610269283304955515092070551540, 34640154270707623660536959321081010, 984420398002534655472050066608012685214, 36099825032617288113038535933108751631313058

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..153

Formula

a(n) = n^(3*n-4) + (1/n) * Sum_{k=1..n-1} k * c_n(k) * e_n(n-k),

where c_n(k) = n^(3*k-3)/k - a(k) for 1 <= k <= n-1,

and e_n(0) = 1, e_n(k) = (n/k) * Sum_{j=1..k} j * c_n(j) * e_n(k-j) for 1 <= k <= n-1.

Prog

(Ruby)
def A395075(n)
  a = [0]
  (1..n).each{|i|
    c = [0] + (1..i - 1).map{|k| i ** (3 * k - 3) / k.to_r - a[k]}
    e = [1]
    (1..i - 1).each{|k| e << i / k.to_r * (1..k).inject(0){|s, j| s + j * c[j] * e[k - j]}}
    a << i ** (3 * i - 4) + (1..i - 1).inject(0){|s, k| s + k * c[k] * e[i - k]}.to_i / i
  }
  a[1..-1]
end
p A395075(20)

Crossrefs

Cf. A319938, A395074.

Sequence in context: A091792 A300595 A395107 * A320418 A090602 A180722

Adjacent sequences: A395072 A395073 A395074 * A395076 A395077 A395078

Keyword

nonn

Author

Seiichi Manyama, Apr 10 2026

Status

approved