A123028 a(n) = (3*n^2 + 3*n + 1)*a(n-2), for n>2, with a(0) = a(1) = 1.

1, 1, 19, 37, 1159, 3367, 147193, 569023, 31940881, 154205233, 10572431611, 61219477501, 4958470425559, 33487054193047, 3128794838527729, 24144166073186887, 2556225383077154593, 22188488621258749153

Offset

0,3

Links

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

Formula

a(n) = n!*b(n), where b(n) = (3*n*(n+1) + 1)*b(n-2)/(n*(n-1)), b(0) = b(1) = 1.

a(n) = A003215(n) * a(n-2), n>2.

Mathematica

a[n_]:= a[n]= If[n<2, 1, (3*n^2 +3*n +1)*a[n-2]]; Table[a[n], {n, 0, 30}]
nxt[{n_, a_, b_}]:={n+1, b, a(3(n+1)^2+3(n+1)+1)}; NestList[nxt, {1, 1, 1}, 20][[All, 2]] (* Harvey P. Dale, Jan 08 2023 *)

Prog

(Magma)
function a(n)
  if n lt 2 then return 1;
  else return (3*n*(n+1) +1)*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 (3*n*(n+1) +1)*a(n-2)
[a(n) for n in (0..30)] # G. C. Greubel, Jul 20 2021

Crossrefs

Cf. A003215, A123025.

Sequence in context: A111441 A144594 A287310 * A067205 A196185 A040342

Adjacent sequences: A123025 A123026 A123027 * A123029 A123030 A123031

Keyword

nonn,easy

Author

Roger L. Bagula, Sep 25 2006

Extensions

Definition replaced by recurrence - the Assoc. Eds. of the OEIS, Mar 27 2010

Edited by G. C. Greubel, Jul 20 2021

Status

approved