A080955 Square array of numbers related to the incomplete gamma function, read by antidiagonals.

1, 1, 1, 1, 2, 2, 1, 3, 5, 6, 1, 4, 10, 16, 24, 1, 5, 17, 38, 65, 120, 1, 6, 26, 78, 168, 326, 720, 1, 7, 37, 142, 393, 872, 1957, 5040, 1, 8, 50, 236, 824, 2208, 5296, 13700, 40320, 1, 9, 65, 366, 1569, 5144, 13977, 37200, 109601, 362880, 1, 10, 82, 538, 2760, 10970, 34960, 100026

Offset: 0

Author

Paul Barry, Feb 26 2003

Keywords

• easy
• nonn
• tabl

Examples

			Array begins:
k=0: 1 1 2 6 24 ...
k=1: 1 2 5 16 65 ...
k=2: 1 3 10 38 168 ...
k=3: 1 4 17 78 393 ...
k=4: 1 5 26 142 824 ...
...
		

Crossrefs

Rows: A000142, A000522, A010842, A053486, A053487, A080954.

Transposed version: A089258.

Programs

Mathematica

T[0, k_] := k!; T[n_, k_] := k!*Sum[n^j/j!, {j, 0, k}];
Table[T[n-k, k], {n, 0, 10}, {k, 0, n}] // Flatten (* Jean-François Alcover, Jan 17 2018 *)

Formula

T(k,n) = n! * Sum{j=0..n} k^j/j!.

E.g.f. of k-th row: exp(k*x)/(1-x).

T(k,n) = A089258(n,k).

Extensions

Corrected by Philippe Deléham, Dec 12 2003