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 A309401 a(n) = A306245(n,n). 2
 1, 1, 3, 43, 5949, 12950796, 586826390263, 669793946192984257, 22558227235537152753501561, 25741074696455818592335996518315259, 1124843928218943684789052411802502269971863691, 2100464404490451025972467064515428575200326254804659324780 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..36 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 *) PROG (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) CROSSREFS Main diagonal of A306245. Cf. A126443, A301419. Sequence in context: A333329 A201173 A290777 * A190637 A287959 A326970 Adjacent sequences:  A309398 A309399 A309400 * A309402 A309403 A309404 KEYWORD nonn AUTHOR Seiichi Manyama, Jul 28 2019 STATUS approved

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Last modified May 7 20:36 EDT 2021. Contains 343652 sequences. (Running on oeis4.)