A385528 E.g.f. A(x) satisfies A(x) = exp(x*A(-2*x)).

1, 1, -3, -47, 1385, 119601, -22345691, -10181013695, 10346973518097, 23934447308323873, -122307331801326167539, -1379021793666951568998159, 33874331587448813081748999673, 1804181313330860398948564389193681, -206892703326367302570264123699846971211

Offset: 0

Author

Seiichi Manyama, Jul 02 2025

Keywords

• sign

Crossrefs

Cf. A000272, A096538, A141369, A385526, A385527, A385529, A385530.

Cf. A015097.

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 A385528(n)
  A(-2, n)
end

Formula

a(0) = 1; a(n) = Sum_{k=0..n-1} (k+1) * (-2)^k * binomial(n-1,k) * a(k) * a(n-1-k).