OFFSET
1,3
FORMULA
EXAMPLE
The array begins:
1, 2, 3, 4, 5, 6, ...
1, 5, 11, 19, 29, 41, ...
1, 12, 41, 94, 177, 296, ...
1, 29, 153, 469, 1097, 2181, ...
1, 70, 571, 2344, 6829, 16186, ...
1, 169, 2131, 11719, 42565, 120421, ...
...
MATHEMATICA
A[n_, k_]:=n! SeriesCoefficient[E^((k-1) x)(k Cosh[Sqrt[k]x]+Sqrt[k]Sinh[Sqrt[k]*x])/k, {x, 0, n}]; Table[A[n-k+1, k], {n, 11}, {k, n}]//Flatten (* or *)
A[n_, k_]:=(Sqrt[k]((k+Sqrt[k]-1)^n+(k-Sqrt[k]-1)^n)+(k+Sqrt[k]-1)^n-(k-Sqrt[k]-1)^n)/(2Sqrt[k]); Simplify[Table[A[n-k+1, k], {n, 11}, {k, n}]]//Flatten
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Stefano Spezia, Oct 25 2023
STATUS
approved