OFFSET
0,3
FORMULA
T(n, k) = Sum_{j=0..k} 2^(k - j)*binomial(k, k - j)*(n - j)!. - Detlef Meya, Aug 12 2024
MATHEMATICA
T[n_, k_] := n! 2^k Hypergeometric1F1[-k, -n, 1/2];
(* Alternative: *)
T[n_, k_] := Sum[2^(k - j)*Binomial[k, k - j]*((n - j)!), {j, 0, k}];
Table[T[n, k], {n, 0, 8}, {k, 0, n}] // Flatten (* Detlef Meya, Aug 12 2024 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Jul 28 2024
STATUS
approved