A131609
Mirror image of triangle in A131606.
Original entry on oeis.org
1, 1, 1, 1, 1, 1, 1, 2, 4, 8, 1, 3, 9, 27, 81, 1, 5, 25, 125, 625, 3125, 1, 8, 64, 512, 4096, 32768, 262144, 1, 13, 169, 2197, 28561, 371293, 4826809, 62748517, 1, 21, 441, 9261, 194481, 4084101, 85766121, 1801088541, 37822859361, 1, 34, 1156, 39304
Offset: 0
Triangle begins:
1
1 1
1 1 1
1 2 4 8
1 3 9 27 81
1 5 25 125 625 3125
1 8 64 512 4096 32768 262144
...
A131606
Triangle read by rows: row n gives coefficients of the polynomial p(x, n) = Sum[Fibonacci[n]^i*x^(n - i), {i, 0, n}].
Original entry on oeis.org
1, 1, 1, 1, 1, 1, 8, 4, 2, 1, 81, 27, 9, 3, 1, 3125, 625, 125, 25, 5, 1, 262144, 32768, 4096, 512, 64, 8, 1, 62748517, 4826809, 371293, 28561, 2197, 169, 13, 1, 37822859361, 1801088541, 85766121, 4084101, 194481, 9261, 441, 21, 1, 60716992766464
Offset: 0
Triangle begins:
{1},
{1, 1},
{1, 1, 1},
{8, 4, 2, 1},
{81, 27, 9, 3, 1},
{3125, 625, 125, 25, 5, 1},
{262144, 32768, 4096, 512, 64, 8, 1},
{62748517, 4826809, 371293, 28561, 2197, 169, 13, 1},
{37822859361, 1801088541, 85766121, 4084101, 194481, 9261, 441, 21, 1},
{60716992766464, 1785793904896, 52523350144, 1544804416, 45435424, 1336336, 39304, 1156, 34, 1},
{253295162119140625, 4605366583984375, 83733937890625, 1522435234375, 27680640625, 503284375, 9150625, 166375, 3025, 55, 1}
-
Clear[p, a] a[n_] = Fibonacci[n]; p[x, 0] = 1; p[x_, n_] := p[x, n] = Sum[a[n]^i*x^(n - i), {i, 0, n}]; Table[p[x, n], {n, 0, 10}]; a0 = Table[CoefficientList[p[x, n], x], {n, 0, 10}]; Flatten[a0] Table[Apply[Plus, CoefficientList[p[x, n], x]], {n, 0, 10}]
Showing 1-2 of 2 results.
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