A385529 E.g.f. A(x) satisfies A(x) = exp(x*A(-3*x)).

1, 1, -5, -152, 15949, 6548656, -9510189137, -48598095401792, 849885323784381337, 50192539805114962349824, -9878895951508580401879879229, -6416836884643090722807370469927936, 13640603845766595275775514993987722683941, 94239467260528503337471761892783659993298198528

Offset: 0

Author

Seiichi Manyama, Jul 02 2025

Keywords

• sign

Crossrefs

Cf. A000272, A096538, A141369, A385526, A385527, A385528, A385530.

Cf. A015098.

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 A385529(n)
  A(-3, n)
end

Formula

a(0) = 1; a(n) = Sum_{k=0..n-1} (k+1) * (-3)^k * binomial(n-1,k) * a(k) * a(n-1-k).