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

Author

Roger L. Bagula, Oct 01 2006

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A000124, A123150.

Programs

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

Mathematica

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

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

Formula

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

Extensions

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

Edited by G. C. Greubel, Jul 17 2023