A249268 - OEIS

A249268

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, 4, 1, -23, -5, 1, -320, -86, 10, 1, 4297, 1102, -152, -11, 1, 92020, 24187, -3122, -281, 16, 1, -1922207, -502151, 66133, 5659, -389, -17, 1, -55746464, -14601740, 1908316, 167254, -10784, -584, 22, 1, 1589338993, 415992316, -54490040, -4745234, 312406, 16048, -734, -23, 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:

4, 1;

-23, -5, 1;

-320, -86, 10, 1;

4297, 1102, -152, -11, 1;

92020, 24187, -3122, -281, 16, 1;

-1922207, -502151, 66133, 5659, -389, -17, 1;

-55746464, -14601740, 1908316, 167254, -10784, -584, 22, 1;

1589338993, 415992316, -54490040, -4745234, 312406, 16048, -734, -23, 1;