A276416 a(n) = a(n-1)*(1 + a(n-1)/a(n-4)), with a(0) = a(1) = a(2) = a(3) = 1.

1, 1, 1, 1, 2, 6, 42, 1806, 1632624, 444245153520, 4698898962968253924720, 12225720633546031105793020748137513851120, 91550929674875028299231929179221527919681972461210779957660001348767546720

Offset: 0

Author

Seiichi Manyama, Sep 02 2016

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..16

Crossrefs

Cf. A133400, A250309.

Programs

Mathematica

RecurrenceTable[{a[n] == a[n - 1] (1 + a[n - 1]/a[n - 4]), a[0] == a[1] == a[2] == a[3] == 1}, a, {n, 0, 12}] (* Michael De Vlieger, Sep 04 2016 *)
nxt[{a_,b_,c_,d_}]:={b,c,d,d(1+d/a)}; NestList[nxt,{1,1,1,1},12][[;;,1]] (* Harvey P. Dale, May 08 2025 *)

Ruby

def A(m, n)
  a = Array.new(m, 1)
  ary = [1]
  while ary.size < n + 1
    break if a[-1] % a[0] > 0
    a = *a[1..-1], a[-1] * (1 + a[-1] / a[0])
    ary << a[0]
  end
  ary
end
def A276416(n)
  A(4, n)
end

Formula

0 = a(n)*(a(n+3) - a(n+4)) + a(n+3)*a(n+3) for all n>=0.

A133400(n) = a(n+1)/a(n).