A375613 - OEIS

%I #6 Aug 30 2024 03:24:03

%S 1,1,5,2,9,41,6,26,113,493,24,102,434,1849,7889,120,504,2118,8906,

%T 37473,157781,720,3000,12504,52134,217442,907241,3786745,5040,20880,

%U 86520,358584,1486470,6163322,25560529,106028861,40320,166320,686160,2831160,11683224,48219366,199040786,821723673,3392923553

%N Triangle read by rows: T(n, k) = n! * 4^k * hypergeom([-k], [-n], 1/4).

%F T(n, k) = Sum_{j=0..k} 4^(k - j)*binomial(k, k - j)*(n - j)!.

%e Triangle starts:

%e [0] 1;

%e [1] 1, 5;

%e [2] 2, 9, 41;

%e [3] 6, 26, 113, 493;

%e [4] 24, 102, 434, 1849, 7889;

%e [5] 120, 504, 2118, 8906, 37473, 157781;

%e [6] 720, 3000, 12504, 52134, 217442, 907241, 3786745;

%e [7] 5040, 20880, 86520, 358584, 1486470, 6163322, 25560529, 106028861;

%e ...

%t T[n_, k_] := Sum[4^(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. A375612, A000142, A056545 (main diagonal).

%Y Cf. A374427, A374428, A375446, A375447, A375597, A375600.

%K nonn,tabl

%O 0,3

%A _Detlef Meya_, Aug 21 2024