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.

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

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

Table of n, a(n) for n=0..44.

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

Cf. A248978, A248976.

Sequence in context: A015155 A009822 A246909 * A245621 A349037 A351710

Adjacent sequences: A249266 A249267 A249268 * A249270 A249271 A249272

Keyword

sign,tabl

Author

Derek Orr, Oct 23 2014

Status

approved