OFFSET
0,2
LINKS
FORMULA
EXAMPLE
Triangle T(n, k) starts:
[0] 1;
[1] 3, 2;
[2] 11, 28, 18;
[3] 25, 184, 351, 192;
[4] 137, 2608, 11097, 16128, 7500;
[5] 147, 6816, 57591, 166912, 193750, 77760;
[6] 1089, 118464, 1865511, 9588736, 20843750, 20062080, 7058940;
[7] 2283, 567936, 16015401, 136921088, 495546875, 858003840, 704129265, 220200960;
MAPLE
R := (n, x) -> add(add(x^j*binomial(u, j)*(j + 1)^n, j = 0..u)/(u + 1), u=0..n):
CoeffList := p -> PolynomialTools:-CoefficientList(p, x):
poly := (n, x) -> ilcm(seq(i, i = 1..n+1)) * R(n, x):
seq(print(CoeffList(poly(n, x))), n = 0..7);
PROG
(SageMath)
def A362995row(n: int) -> list[int]:
s = add((1 / (u + 1)) * add(x^j * binomial(u, j) * (j + 1)^n
for j in (0..u)) for u in (0..n))
l = lcm(i + 1 for i in (0..n))
return (s * l).list()
for n in (0..7): print(A362995row(n))
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, May 14 2023
STATUS
approved