A249269 - OEIS

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

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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:

-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;