|
Search: id:A099028
|
|
|
| A099028 |
|
Euler-Seidel matrix T(k,n) with start sequence e.g.f. 2x/(1+e^(2x)), read by antidiagonals. |
|
+0
5
|
|
| 0, 1, 1, 0, -1, -2, -3, -3, -2, 0, 0, 3, 6, 8, 8, 25, 25, 22, 16, 8, 0, 0, -25, -50, -72, -88, -96, -96, -427, -427, -402, -352, -280, -192, -96, 0, 0, 427, 854, 1256, 1608, 1888, 2080, 2176, 2176, 12465, 12465, 12038, 11184, 9928, 8320, 6432, 4352, 2176
(list; table; graph; listen)
|
|
|
OFFSET
|
0,6
|
|
|
COMMENT
|
In an Euler-Seidel matrix, the rows are consecutive pairwise sums and the columns consecutive differences, with the first column the inverse binomial transform of the start sequence.
|
|
LINKS
|
D. Dumont, Matrices d'Euler-Seidel, Sem. Loth. Comb. B05c (1981) 59-78.
|
|
FORMULA
|
Recurrence: T(k, n) = T(k-1, n) + T(k-1, n+1).
|
|
EXAMPLE
|
0,1,-2,0,8,0,
1,-1,-2,8,8,-96,
0,-3,6,16,-88,-192,
-3,3,22,-72,-280,1888,
0,25,-50,-352,1608,8320,
25,-25,-402,1256,9928,-58080,
|
|
CROSSREFS
|
First column (odd part) is A009843, main diagonal is in A099029. Antidiagonal sums are in A065619. Cf. A009752.
Sequence in context: A123948 A131012 A083057 this_sequence A077869 A076585 A022906
Adjacent sequences: A099025 A099026 A099027 this_sequence A099029 A099030 A099031
|
|
KEYWORD
|
sign,tabl
|
|
AUTHOR
|
Ralf Stephan, Sep 27 2004
|
|
|
Search completed in 0.002 seconds
|
