A385530 E.g.f. A(x) satisfies A(x) = exp(x*A(-4*x)).

1, 1, -7, -359, 90705, 116586321, -715618113143, -20523234900205911, 2689857437569063003169, 1586566688643256394542888225, -4159073515698730238218108546470759, -47972197129364591236078587520718376138951, 2414519164037893898620724924577882591112859773297

Offset: 0

Author

Seiichi Manyama, Jul 02 2025

Keywords

• sign

Crossrefs

Cf. A000272, A096538, A141369, A385526, A385527, A385528, A385529.

Cf. A015099.

Programs

Ruby

def ncr(n, r)
  return 1 if r == 0
  (n - r + 1..n).inject(:*) / (1..r).inject(:*)
end
def A(q, n)
  ary = [1]
  (1..n).each{|i| ary << (0..i - 1).inject(0){|s, j| s + (j + 1) * q ** j * ncr(i - 1, j) * ary[j] * ary[i - 1 - j]}}
  ary
end
def A385530(n)
  A(-4, n)
end

Formula

a(0) = 1; a(n) = Sum_{k=0..n-1} (k+1) * (-4)^k * binomial(n-1,k) * a(k) * a(n-1-k).