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%I #6 Oct 13 2012 13:35:59
%S 1,1,1,1,1,1,8,4,2,1,81,27,9,3,1,3125,625,125,25,5,1,262144,32768,
%T 4096,512,64,8,1,62748517,4826809,371293,28561,2197,169,13,1,
%U 37822859361,1801088541,85766121,4084101,194481,9261,441,21,1,60716992766464
%N Triangle read by rows: row n gives coefficients of the polynomial p(x, n) = Sum[Fibonacci[n]^i*x^(n - i), {i, 0, n}].
%C Row sums give A131612.
%e Triangle begins:
%e {1},
%e {1, 1},
%e {1, 1, 1},
%e {8, 4, 2, 1},
%e {81, 27, 9, 3, 1},
%e {3125, 625, 125, 25, 5, 1},
%e {262144, 32768, 4096, 512, 64, 8, 1},
%e {62748517, 4826809, 371293, 28561, 2197, 169, 13, 1},
%e {37822859361, 1801088541, 85766121, 4084101, 194481, 9261, 441, 21, 1},
%e {60716992766464, 1785793904896, 52523350144, 1544804416, 45435424, 1336336, 39304, 1156, 34, 1},
%e {253295162119140625, 4605366583984375, 83733937890625, 1522435234375, 27680640625, 503284375, 9150625, 166375, 3025, 55, 1}
%t 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}]
%Y Cf. A130321, A000045, A131609.
%K nonn,tabl
%O 0,7
%A _Roger L. Bagula_ and _Gary W. Adamson_, May 27 2008
%E Edited by _N. J. A. Sloane_, May 27 2008