|
| |
|
|
A081114
|
|
Triangle read by rows of T(n,k)=n*T(n-1,k)+n-k starting at T(n,n)=0.
|
|
0
| |
|
|
0, 1, 0, 4, 1, 0, 15, 5, 1, 0, 64, 23, 6, 1, 0, 325, 119, 33, 7, 1, 0, 1956, 719, 202, 45, 8, 1, 0, 13699, 5039, 1419, 319, 59, 9, 1, 0, 109600, 40319, 11358, 2557, 476, 75, 10, 1, 0, 986409, 362879, 102229, 23019, 4289, 679, 93, 11, 1, 0, 9864100, 3628799, 1022298
(list; table; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,4
|
|
|
COMMENTS
| Taking the triangle into negative values of n and k would produce results close to (k+1)*e*n! - 1, i.e. one less than multiples of A000522 for nonnegative n.
|
|
|
FORMULA
| For k>0, T(n, k)=ceiling[ (A001339(k-1)/(k-1)! - (k-1)*e) *n! - 1] where A001339(k-1)=ceiling[(k-1)!*(k-1)*e for k>1]. T(n, 0)=floor[e*n! - 1] for n>0; T(n, 1)=n!-1. T(n, n)=0; T(n, n-1)=n+2; T(n, n-2)=n^2+3n+5=A027688(n+1).
|
|
|
EXAMPLE
| Rows start: 0; 1,0; 4,1,0; 15,5,1,0; 64,23,6,1,0; 325,119,33,7,1,0; etc.
|
|
|
CROSSREFS
| Columns include A007526 and A033312.
Sequence in context: A048516 A060638 A007789 * A069018 A156811 A130636
Adjacent sequences: A081111 A081112 A081113 * A081115 A081116 A081117
|
|
|
KEYWORD
| nonn,tabl
|
|
|
AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), Apr 16 2003
|
| |
|
|
