OFFSET
1,3
COMMENTS
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..11325 (rows 1 <= n <= 150, flattened.)
FORMULA
T(n,k) = Sum_{j=1..k-1} (n-j-1)!*(k-j)*binomial(k-1,j-1) for k < n;
T(n,n) = (n-1)!*Sum_{j=0..n-1} 1/j!.
EXAMPLE
T(4,3)=6 because we have 3124, 3142, 3214, 3241, 1324 and 2314.
Triangle starts:
1;
0, 2;
0, 1, 5;
0, 2, 6, 16;
0, 6, 16, 33, 65;
0, 24, 60, 114, 196, 326;
MAPLE
T:=proc(n, k): if k < n then sum(factorial(k-1)*factorial(n-j-1)/(factorial(j-1)*factorial(k-j-1)), j=1..k-1) elif k = n then factorial(n-1)*(sum(1/factorial(j), j = 0 .. n-1)) else 0 end if end proc: for n to 9 do seq(T(n, k), k=1..n) end do; # yields sequence in triangular form
MATHEMATICA
Table[If[k < n, Sum[(n - j - 1)!*(k - j)*Binomial[k - 1, j - 1], {j, k - 1}], (n - 1)!*Sum[1/j!, {j, 0, n - 1}]], {n, 9}, {k, n}] // Flatten (* Michael De Vlieger, Nov 15 2019 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Emeric Deutsch, Nov 22 2007
STATUS
approved