A375597 - OEIS

%I #6 Aug 21 2024 05:34:54

%S 1,1,1,2,4,10,6,14,34,82,24,60,152,388,1000,120,312,816,2144,5656,

%T 14968,720,1920,5136,13776,37040,99808,269488,5040,13680,37200,101328,

%U 276432,755216,2066032,5659120,40320,110880,305280,841440,2321664,6412128,17725952,49045792,135819136

%N Triangle read by rows: T(n, k) = n! * 3^k * hypergeom([-k], [-n], -2/3).

%F T(n, k) = (-2)^k*Sum_{j=0..k} (-3/2)^(k - j)*binomial(k, k - j)*(n - j)!.

%e Triangle starts:

%e [0] 1;

%e [1] 1, 1;

%e [2] 2, 4, 10;

%e [3] 6, 14, 34, 82;

%e [4] 24, 60, 152, 388, 1000;

%e [5] 120, 312, 816, 2144, 5656, 14968;

%e [6] 720, 1920, 5136, 13776, 37040, 99808, 269488;

%e [7] 5040, 13680, 37200, 101328, 276432, 755216, 2066032, 5659120;

%e ...

%t T[n_, k_] := (-2)^k*Sum[(-3/2)^(k - j)*Binomial[k, k - j]*(n - j)!, {j, 0, k}];

%t Table[T[n, k], {n, 0, 8}, {k, 0, n}] // Flatten

%Y Cf. A375600, A000142.

%Y Cf. A374427, A374428, A375446, A375447.

%K nonn,tabl

%O 0,4

%A _Detlef Meya_, Aug 20 2024