A123145 a(1) = 1, a(n) = a(n-1) if n == 1 (mod 4), otherwise a(n) = n * a(n-1) for n >= 2.

1, 2, 6, 24, 24, 144, 1008, 8064, 8064, 80640, 887040, 10644480, 10644480, 149022720, 2235340800, 35765452800, 35765452800, 643778150400, 12231784857600, 244635697152000, 244635697152000, 5381985337344000, 123785662758912000, 2970855906213888000

Offset

1,2

Comments

Terms which repeat appear to be denominators of g.f. 0F2(--; 1/2, 3/4; z^4/64), which begin 24, 8064, 10644480, 35765452800, ... - Benedict W. J. Irwin, Jun 15 2018

Links

G. C. Greubel, Table of n, a(n) for n = 1..500

Formula

Conjecture: E.g.f.: E(x)=d(G(0))/dx where G(k) = 1 + x/(4*k+1 - x*(4*k+1)/(1 + x - x/(1 + x - x/(x + 1/G(k+1) )))), or shift on 1 left G(0); (continued fraction,5-step). - Sergei N. Gladkovskii, Nov 26 2012

Maple

a:= proc(n) option remember; `if`(n=0, 1,
      `if`(irem(n, 4)=1, 1, n)*a(n-1))
    end:
seq(a(n), n=1..24);  # Alois P. Heinz, Jul 16 2023

Mathematica

a[n_]:= a[n]= If[n==1, 1, If[Mod[n, 4]==1, a[n-1], n*a[n-1]]];
Table[a[n], {n, 30}]

Prog

(Magma)
function a(n) // a = A123145
  if n eq 1 then return 1;
  elif (n mod 4) eq 1 then return a(n-1);
  else return n*a(n-1);
  end if;
end function;
[a(n): n in [1..40]]; // G. C. Greubel, Jul 16 2023
(SageMath)
def a(n): # A123145
    if (n==1): return 1
    elif (n%4==1): return a(n-1)
    else: return n*a(n-1)
[a(n) for n in range(1, 41)] # G. C. Greubel, Jul 16 2023

Crossrefs

Cf. A007559, A007696.

Sequence in context: A060068 A099732 A118381 * A232981 A304039 A246454

Adjacent sequences: A123142 A123143 A123144 * A123146 A123147 A123148

Keyword

nonn

Author

Roger L. Bagula, Oct 01 2006

Extensions

Edited by N. J. A. Sloane, Oct 04 2006

More terms from Bruno Berselli, Nov 27 2012

Status

approved