A144446 - OEIS

%I #11 Mar 06 2022 04:48:06

%S 1,2,1,7,2,1,30,10,2,1,157,64,13,2,1,972,532,110,16,2,1,6961,5448,

%T 1249,168,19,2,1,56660,66440,17816,2416,238,22,2,1,516901,941056,

%U 306619,44160,4141,320,25,2,1,5225670,15189776,6185828,981184,92292,6532,414,28,2,1

%N Array t(n, k) = (k*(n-1) +2-k)*t(n-1, k) + k*t(n-2, k), with t(1, k) = 1, t(2, k) = 2, read by antidiagonals.

%H G. C. Greubel, <a href="/A144446/b144446.txt">Antidiagonals n = 1..50, flattened</a>

%F T(n, k) = t(n-k+1, k), where t(n, k) = (k*(n-1) +2-k)*t(n-1, k) + k*t(n-2, k) with t(1, k) = 1, t(2, k) = 2.

%F T(n, 1) = A001053(n+1).

%F T(n, k) = (k*(n-k)+2-k)*T(n-1, k) + k*T(n-2, k) with T(n, n-1) = 2, T(n, n) = 1 (as a triangle). - _G. C. Greubel_, Mar 05 2022

%e Array t(n,k) begins as:

%e     1,    1,     1,     1,     1,      1, ...;

%e     2,    2,     2,     2,     2,      2, ...;

%e     7,   10,    13,    16,    19,     22, ...;

%e    30,   64,   110,   168,   238,    320, ...;

%e   157,  532,  1249,  2416,  4141,   6532, ...;

%e   972, 5448, 17816, 44160, 92292, 171752, ...;

%e Antidiagonal triangle T(n,k) begins as:

%e         1;

%e         2,        1;

%e         7,        2,       1;

%e        30,       10,       2,      1;

%e       157,       64,      13,      2,     1;

%e       972,      532,     110,     16,     2,    1;

%e      6961,     5448,    1249,    168,    19,    2,   1;

%e     56660,    66440,   17816,   2416,   238,   22,   2,  1;

%e    516901,   941056,  306619,  44160,  4141,  320,  25,  2, 1;

%e   5225670, 15189776, 6185828, 981184, 92292, 6532, 414, 28, 2, 1;

%t t[n_, k_]:= t[n, k]= If[n<3, n, (k*(n-1) +2-k)*t[n-1,k] + k*t[n-2,k]];

%t T[n_, k_]:= t[n-k+1,k];

%t Table[T[n, k], {n, 12}, {k,n}]//Flatten (* modified by _G. C. Greubel_, Mar 05 2022 *)

%o (Magma)

%o function T(n,k) // triangle form; A144446

%o   if k gt n-2 then return n-k+1;

%o   else return (k*(n-k)+2-k)*T(n-1, k) + k*T(n-2, k);

%o   end if; return T;

%o end function;

%o [T(n,k): k in [1..n], n in [1..12]]; // _G. C. Greubel_, Mar 05 2022

%o (Sage)

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

%o def A144446(n,k): return t(n-k+1,k)

%o flatten([[A144446(n,k) for k in (1..n)] for n in (1..12)]) # _G. C. Greubel_, Mar 05 2022

%Y Cf. A144431, A144432, A144435, A144436, A144438, A144439, A144440, A144441, A144442, A144443, A144444, A144445, A144447.

%Y Cf. A001053.

%K nonn,tabl

%O 1,2

%A _Roger L. Bagula_ and _Gary W. Adamson_, Oct 05 2008

%E Edited by _G. C. Greubel_, Mar 05 2022