A123028 - OEIS

%I #16 Sep 15 2024 13:42:04

%S 1,1,19,37,1159,3367,147193,569023,31940881,154205233,10572431611,

%T 61219477501,4958470425559,33487054193047,3128794838527729,

%U 24144166073186887,2556225383077154593,22188488621258749153

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

%H G. C. Greubel, <a href="/A123028/b123028.txt">Table of n, a(n) for n = 0..400</a>

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

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

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

%t 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 *)

%o (Magma)

%o function a(n)

%o   if n lt 2 then return 1;

%o   else return (3*n*(n+1) +1)*a(n-2);

%o   end if; return a;

%o end function;

%o [a(n): n in [0..30]]; // _G. C. Greubel_, Jul 20 2021

%o (Sage)

%o def a(n): return 1 if (n<2) else (3*n*(n+1) +1)*a(n-2)

%o [a(n) for n in (0..30)] # _G. C. Greubel_, Jul 20 2021

%Y Cf. A003215, A123025.

%K nonn,easy

%O 0,3

%A _Roger L. Bagula_, Sep 25 2006

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

%E Edited by _G. C. Greubel_, Jul 20 2021