A292606 - OEIS

A292606

Triangle read by rows, coefficients of generalized Eulerian polynomials F_{4;n}(x).

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

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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