A123026 a(n) = n!*b(n), where b(n) = ((n-1)^2 - 2)*b(n-2)/(n*(n-1)) and b(0) = b(1) = 1.

1, 1, -1, 2, -7, 28, -161, 952, -7567, 59024, -597793, 5784352, -71137367, 821377984, -11879940289, 159347328896, -2649226684447, 40474221539584, -760328058436289, 13032699335746048, -272957772978627751, 5187014335626927104, -119828462337617582689, 2500140909772178864128

Offset

0,4

Links

G. C. Greubel, Table of n, a(n) for n = 0..400

Formula

a(n) = n!*b(n), where b(n) = (n^2 - 2*n - 1)*b(n) and b(0) = b(1) = 1.

a(n) = ((n-1)^2 - 2)*a(n-2) with a(0) = a(1) = 1. - G. C. Greubel, Jul 20 2021

Mathematica

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

Prog

(Magma)
function a(n)
  if n lt 2 then return 1;
  else return ((n-1)^2 -2)*a(n-2);
  end if; return a;
end function;
[a(n): n in [0..30]]; // G. C. Greubel, Jul 20 2021
(Sage)
def a(n): return 1 if (n<2) else ((n-1)^2 -2)*a(n-2)
[a(n) for n in (0..30)] # G. C. Greubel, Jul 20 2021

Crossrefs

Cf. A123025.

Sequence in context: A296726 A334613 A365559 * A013011 A013181 A191478

Adjacent sequences: A123023 A123024 A123025 * A123027 A123028 A123029

Keyword

sign

Author

Roger L. Bagula, Sep 24 2006

Extensions

Edited by N. J. A. Sloane, Oct 01 2006

Edited by G. C. Greubel, Jul 20 2021

Status

approved