|
| |
|
|
A249269
|
|
Triangle read by rows: T(n,k) is the coefficient A_k in the transformation Sum_{k=0..n} x^k = Sum_{k=0..n} A_k*(x-3*(-1)^k)^k.
|
|
0
|
|
|
|
1, -2, 1, -29, 7, 1, 268, -74, -8, 1, 4885, -1262, -170, 13, 1, -82838, 21823, 2800, -257, -14, 1, -2097065, 548161, 72055, -6197, -419, 19, 1, 51727192, -13551428, -1770128, 155398, 9976, -548, -20, 1, 1696812649, -444145484, -58168484, 5067886, 333166, -17180, -776, 25, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
COMMENTS
|
Consider the transformation 1 + x + x^2 + x^3 + ... + x^n = A_0*(x-3)^0 + A_1*(x+3)^1 + A_2*(x-3)^2 + A_3*(x+3)^3 + ... + A_n*(x-3*(-1)^n)^n. This sequence gives A_0, ... A_n as the entries in the n-th row of this triangle, starting at n = 0.
|
|
|
LINKS
|
|
|
|
EXAMPLE
|
Triangle starts:
1;
-2, 1;
-29, 7, 1;
268, -74, -8, 1;
4885, -1262, -170, 13, 1;
-82838, 21823, 2800, -257, -14, 1;
-2097065, 548161, 72055, -6197, -419, 19, 1;
51727192, -13551428, -1770128, 155398, 9976, -548, -20, 1;
1696812649, -444145484, -58168484, 5067886, 333166, -17180, -776, 25, 1;
...
|
|
|
PROG
|
(PARI) a(n, j, L)=if(j==n, return(1)); if(j!=n, return(1-sum(i=1, n-j, (-L)^i*(-1)^(i*j)*binomial(i+j, i)*a(n, i+j, L))))
for(n=0, 10, for(j=0, n, print1(a(n, j, -3), ", ")))
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
