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A292605 Triangle read by rows, coefficients of generalized Eulerian polynomials F_{3;n}(x). 3
1, 1, 0, 19, 1, 0, 1513, 166, 1, 0, 315523, 52715, 1361, 1, 0, 136085041, 30543236, 1528806, 10916, 1, 0, 105261234643, 29664031413, 2257312622, 42421946, 87375, 1, 0, 132705221399353, 45011574747714, 4637635381695, 153778143100, 1156669095, 699042, 1, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,4
COMMENTS
See the comments in A292604.
LINKS
FORMULA
F_{3; n}(x) = Sum_{k=0..n} A278073(n, k)*(x-1)^(n-k) for n>0 and F_{3; 0}(x) = 1.
EXAMPLE
Triangle starts:
[n\k][ 0 1 2 3 4 5]
--------------------------------------------------
[0][ 1]
[1][ 1, 0]
[2][ 19, 1, 0]
[3][ 1513, 166, 1, 0]
[4][ 315523, 52715, 1361, 1, 0]
[5][ 136085041, 30543236, 1528806, 10916, 1, 0]
MAPLE
Coeffs := f -> PolynomialTools:-CoefficientList(expand(f), x):
A292605_row := proc(n) if n = 0 then return [1] fi;
add(A278073(n, k)*(x-1)^(n-k), k=0..n); [op(Coeffs(%)), 0] end:
for n from 0 to 6 do A292605_row(n) od;
PROG
(Sage) # uses[A278073_row from A278073]
def A292605_row(n):
if n == 0: return [1]
L = A278073_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(A292605_row(n))
CROSSREFS
F_{0} = A129186, F_{1} = A173018, F_{2} = A292604, F_{3} is this triangle, F_{4} = A292606.
First column: A002115. Row sums: A014606. Alternating row sums: A292609.
Sequence in context: A366110 A317447 A202582 * A338873 A040365 A040366
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Sep 20 2017
STATUS
approved

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Last modified March 29 00:26 EDT 2024. Contains 371264 sequences. (Running on oeis4.)