cp's OEIS Frontend

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

%I A309401 #17 Nov 14 2020 09:47:56
%S A309401 1,1,3,43,5949,12950796,586826390263,669793946192984257,
%T A309401 22558227235537152753501561,25741074696455818592335996518315259,
%U A309401 1124843928218943684789052411802502269971863691,2100464404490451025972467064515428575200326254804659324780
%N A309401 a(n) = A306245(n,n).
%H A309401 Seiichi Manyama, <a href="/A309401/b309401.txt">Table of n, a(n) for n = 0..36</a>
%p A309401 b:= proc(n, k) option remember; `if`(n=0, 1,
%p A309401       add(k^j*binomial(n-1, j)*b(j, k), j=0..n-1))
%p A309401     end:
%p A309401 a:= n-> b(n$2):
%p A309401 seq(a(n), n=0..12);  # _Alois P. Heinz_, Jul 28 2019
%t A309401 b[0, _] = 1;
%t A309401 b[n_, k_] := b[n, k] = Sum[k^j Binomial[n-1, j] b[j, k], {j, 0, n-1}];
%t A309401 a[n_] := b[n, n];
%t A309401 a /@ Range[0, 12] (* _Jean-François Alcover_, Nov 14 2020, after _Alois P. Heinz_ *)
%o A309401 (Ruby)
%o A309401 def ncr(n, r)
%o A309401   return 1 if r == 0
%o A309401   (n - r + 1..n).inject(:*) / (1..r).inject(:*)
%o A309401 end
%o A309401 def A(k, n)
%o A309401   ary = [1]
%o A309401   (1..n).each{|i| ary << (0..i - 1).inject(0){|s, j| s + k ** j * ncr(i - 1, j) * ary[j]}}
%o A309401   ary
%o A309401 end
%o A309401 def A309401(n)
%o A309401   (0..n).map{|i| A(i, i)}
%o A309401 end
%o A309401 p A309401(20)
%Y A309401 Main diagonal of A306245.
%Y A309401 Cf. A126443, A301419.
%K A309401 nonn
%O A309401 0,3
%A A309401 _Seiichi Manyama_, Jul 28 2019