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

0,5

Links

Table of n, a(n) for n=0..62.

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).

Example

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 ...
...

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 *)

Crossrefs

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

Transposed version: A089258.

Sequence in context: A071944 A309495 A388788 * A340108 A340107 A125231

Adjacent sequences: A080952 A080953 A080954 * A080956 A080957 A080958

Keyword

easy,nonn,tabl

Author

Paul Barry, Feb 26 2003

Extensions

Corrected by Philippe Deléham, Dec 12 2003

Status

approved