A361042 Triangle read by rows: T(n, k) = Sum_{j=0..n} j! * binomial(n - j, n - k).

1, 1, 2, 1, 3, 4, 1, 4, 7, 10, 1, 5, 11, 17, 34, 1, 6, 16, 28, 51, 154, 1, 7, 22, 44, 79, 205, 874, 1, 8, 29, 66, 123, 284, 1079, 5914, 1, 9, 37, 95, 189, 407, 1363, 6993, 46234, 1, 10, 46, 132, 284, 596, 1770, 8356, 53227, 409114, 1, 11, 56, 178, 416, 880, 2366, 10126, 61583, 462341, 4037914

Offset

0,3

Links

Table of n, a(n) for n=0..65.

Example

Triangle T(n, k) starts:
[0] 1;
[1] 1,  2;
[2] 1,  3,  4;
[3] 1,  4,  7,  10;
[4] 1,  5, 11,  17,  34;
[5] 1,  6, 16,  28,  51, 154;
[6] 1,  7, 22,  44,  79, 205,  874;
[7] 1,  8, 29,  66, 123, 284, 1079, 5914;
[8] 1,  9, 37,  95, 189, 407, 1363, 6993, 46234;
[9] 1, 10, 46, 132, 284, 596, 1770, 8356, 53227, 409114.

Crossrefs

Cf. A003422 (main diagonal), A014144 (subdiagonal), A152689, A233449 (row sums), A133942 (alternating row sums), A293468 (central row).

Sequence in context: A008949 A076832 A078925 * A072506 A188236 A181851

Adjacent sequences: A361039 A361040 A361041 * A361043 A361044 A361045

Keyword

nonn,tabl

Author

Peter Luschny, Mar 13 2023

Status

approved