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 A139167 Triangle T(n,k) read by rows: the coefficient [x^k] of the polynomial (n-1)! *sum_{i=0..n} Fibonacci(i)*binomial(x,n-i), read by rows, 0<=k
 1, 1, 1, 4, 1, 1, 18, 11, 0, 1, 120, 50, 23, -2, 1, 960, 494, 65, 45, -5, 1, 9360, 4344, 1354, -15, 85, -9, 1, 105840, 51876, 10444, 3409, -350, 154, -14, 1, 1370880, 653232, 172444, 13300, 8729, -1232, 266, -20, 1, 19958400, 9654480, 2194380, 483272, -13923, 22449, -3150, 438, -27, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Row sums are 1, 2, 6, 30, 192, 1560, 15120, 171360, 2217600, 32296320,... (see A078700) REFERENCES Brendan Hassett, Introduction to algebraic Geometry,Cambridge University Press. New York,2007, page 229 LINKS EXAMPLE 1; 1, 1; 4, 1, 1; 18, 11, 0, 1; 120, 50, 23, -2, 1; 960, 494, 65, 45, -5, 1; 9360, 4344, 1354, -15,85, -9, 1; 105840, 51876, 10444, 3409, -350, 154, -14, 1; 1370880, 653232, 172444, 13300, 8729, -1232, 266, -20, 1; 19958400, 9654480, 2194380, 483272, -13923, 22449, -3150, 438, -27, 1; MAPLE B := proc(x, k)     mul( (x-i+1)/i, i=1..k) ; end proc: A139167 := proc(n, k)     local f, i ;     f := 0 ;     for i from 0 to n do         f := f+combinat[fibonacci](i)*B(x, n-i) ;     end do;     %*(n-1)! ;     coeftayl(%, x=0, k) ; end proc: # R. J. Mathar, May 08 2013 MATHEMATICA Clear[a, p, x] a[0] = 0; a[1] = 1; a[n_] := a[n] = a[n - 1] + a[n - 2]; p[x, 0] = a[0]; p[x_, n_] := p[x, n] = Sum[a[i]*Binomial[x, n - i], {i, 0, n}]; Table[If[n > 0, ExpandAll[(n - 1)!*p[x, n]], 0], {n, 0, 10}]; a = Table[CoefficientList[If[n > 0, ExpandAll[(n - 1)!*p[x, n]], 0], x], {n, 0, 10}]; Flatten[a] Table[Apply[Plus, CoefficientList[If[n > 0, ExpandAll[(n - 1)!*p[x, n]], 0], x]], {n, 0, 10}] CROSSREFS Cf. A000045. Sequence in context: A034802 A177262 A203092 * A211709 A323849 A254442 Adjacent sequences:  A139164 A139165 A139166 * A139168 A139169 A139170 KEYWORD tabl,sign AUTHOR Roger L. Bagula, Jun 05 2008 EXTENSIONS Edited by R. J. Mathar, May 08 2013 STATUS approved

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Last modified April 7 15:56 EDT 2020. Contains 333306 sequences. (Running on oeis4.)