A309401 a(n) = A306245(n,n).

1, 1, 3, 43, 5949, 12950796, 586826390263, 669793946192984257, 22558227235537152753501561, 25741074696455818592335996518315259, 1124843928218943684789052411802502269971863691, 2100464404490451025972467064515428575200326254804659324780

Offset: 0

Author

Seiichi Manyama, Jul 28 2019

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..36

Crossrefs

Main diagonal of A306245.

Cf. A126443, A301419.

Programs

Maple

b:= proc(n, k) option remember; `if`(n=0, 1,
      add(k^j*binomial(n-1, j)*b(j, k), j=0..n-1))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..12);  # Alois P. Heinz, Jul 28 2019

Mathematica

b[0, _] = 1;
b[n_, k_] := b[n, k] = Sum[k^j Binomial[n-1, j] b[j, k], {j, 0, n-1}];
a[n_] := b[n, n];
a /@ Range[0, 12] (* Jean-François Alcover, Nov 14 2020, after Alois P. Heinz *)

Ruby

def ncr(n, r)
  return 1 if r == 0
  (n - r + 1..n).inject(:*) / (1..r).inject(:*)
end
def A(k, n)
  ary = [1]
  (1..n).each{|i| ary << (0..i - 1).inject(0){|s, j| s + k ** j * ncr(i - 1, j) * ary[j]}}
  ary
end
def A309401(n)
  (0..n).map{|i| A(i, i)}
end
p A309401(20)