A144446 - OEIS

A144446

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.

%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