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 A292606 Triangle read by rows, coefficients of generalized Eulerian polynomials F_{4;n}(x). 3
 1, 1, 0, 69, 1, 0, 33661, 988, 1, 0, 60376809, 2669683, 16507, 1, 0, 288294050521, 17033188586, 212734266, 261626, 1, 0, 3019098162602349, 223257353561605, 4297382231090, 17634518610, 4196345, 1, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS See the comments in A292604. LINKS Table of n, a(n) for n=0..27. FORMULA F_{4; n}(x) = Sum_{k=0..n} A278074(n, k)*(x-1)^(n-k) for n>0 and F_{4; 0}(x) = 1. EXAMPLE Triangle starts: [n\k][ 0 1 2 3 4 5] -------------------------------------------------- [0] [ 1] [1] [ 1, 0] [2] [ 69, 1, 0] [3] [ 33661, 988, 1, 0] [4] [ 60376809, 2669683, 16507, 1, 0] [5] [288294050521, 17033188586, 212734266, 261626, 1, 0] MAPLE Coeffs := f -> PolynomialTools:-CoefficientList(expand(f), x): A292606_row := proc(n) if n = 0 then return [1] fi; add(A278074(n, k)*(x-1)^(n-k), k=0..n); [op(Coeffs(%)), 0] end: for n from 0 to 6 do A292606_row(n) od; PROG (Sage) # uses[A278074_row from A278074] def A292606_row(n): if n == 0: return [1] L = A278074_row(n) S = sum(L[k]*(x-1)^(n-k) for k in (0..n)) return expand(S).list() + [0] for n in (0..5): print(A292606_row(n)) CROSSREFS F_{0} = A129186, F_{1} = A173018, F_{2} = A292604, F_{3} = A292605, F_{4} is this triangle. First column: A211212. Row sums: A014608. Alternating row sums: A292607. Cf. A181985. Sequence in context: A203757 A159385 A116196 * A036181 A033389 A265189 Adjacent sequences: A292603 A292604 A292605 * A292607 A292608 A292609 KEYWORD nonn,tabl AUTHOR Peter Luschny, Sep 26 2017 STATUS approved

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Last modified September 7 16:30 EDT 2024. Contains 375749 sequences. (Running on oeis4.)