A123151 a(n) = A000124(n)*a(n-3) for n > 2, otherwise n!.

1, 1, 2, 7, 11, 32, 154, 319, 1184, 7084, 17864, 79328, 559636, 1643488, 8408768, 67715956, 225157856, 1294950272, 11647144432, 43005150496, 273234507392, 2702137508224, 10923308225984, 75685958547584, 813343389975424, 3560998481670784, 26641457408749568

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..500

Formula

a(n) = n! for n < 3, otherwise a(n) = A000124(n)*a(n-3), where A000124(n) = (n^2 + n + 2)/2.

Mathematica

a[n_]:= a[n]= If[n<3, n!, (1/2)*(n^2+n+2)*a[n-3]];
Table[a[n], {n, 0, 30}]

Prog

(Magma)
function a(n) // a = A123151
  if n le 2 then return Factorial(n);
  else return (n^2+n+2)*a(n-3)/2;
  end if;
end function;
[a(n): n in [0..30]]; // G. C. Greubel, Jul 17 2023
(SageMath)
@CachedFunction # a = A123151
def a(n): return factorial(n) if (n<3) else (n^2+n+2)*a(n-3)/2
[a(n) for n in (0..30)] # G. C. Greubel, Jul 17 2023

Crossrefs

Cf. A000124, A123150.

Sequence in context: A336342 A284354 A228076 * A371201 A026133 A026162

Adjacent sequences: A123148 A123149 A123150 * A123152 A123153 A123154

Keyword

nonn,easy

Author

Roger L. Bagula, Oct 01 2006

Extensions

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

Edited by G. C. Greubel, Jul 17 2023

Status

approved