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 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}]. 2
 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,7 COMMENTS Row sums give A131612. LINKS EXAMPLE 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} MATHEMATICA 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}] CROSSREFS Cf. A130321, A000045, A131609. Sequence in context: A133839 A080828 A131916 * A033328 A097529 A114321 Adjacent sequences:  A131603 A131604 A131605 * A131607 A131608 A131609 KEYWORD nonn,tabl AUTHOR Roger L. Bagula and Gary W. Adamson, May 27 2008 EXTENSIONS Edited by N. J. A. Sloane, May 27 2008 STATUS approved

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