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A362997
Triangle read by rows. T(n, k) = denominator([x^k] R(n, n, x)), where R(n, k, x) = Sum_{u=0..k} ( Sum_{j=0..u} x^j * binomial(u, j) * (j + 1)^n ) / (u + 1).
2
1, 2, 1, 6, 3, 1, 12, 3, 4, 1, 60, 15, 20, 5, 1, 20, 5, 20, 15, 6, 1, 140, 35, 140, 105, 42, 7, 1, 280, 35, 280, 105, 168, 7, 8, 1, 2520, 315, 280, 315, 504, 7, 72, 9, 1, 2520, 315, 280, 315, 504, 35, 360, 45, 10, 1, 27720, 3465, 3080, 3465, 5544, 385, 3960, 495, 110, 11, 1
OFFSET
0,2
FORMULA
T(n, k) = lcm(1, 2, ..., n+1) * A362996(n, k) / A362995(n, k).
EXAMPLE
Triangle T(n, k) starts:
[0] 1;
[1] 2, 1;
[2] 6, 3, 1;
[3] 12, 3, 4, 1;
[4] 60, 15, 20, 5, 1;
[5] 20, 5, 20, 15, 6, 1;
[6] 140, 35, 140, 105, 42, 7, 1;
[7] 280, 35, 280, 105, 168, 7, 8, 1;
[8] 2520, 315, 280, 315, 504, 7, 72, 9, 1;
[9] 2520, 315, 280, 315, 504, 35, 360, 45, 10, 1;
PROG
(SageMath)
def R(n, k, x):
return add((1 / (u + 1)) * add(x^j * binomial(u, j) * (j + 1)^n
for j in (0..u)) for u in (0..k))
def A362997row(n: int) -> list[int]:
return [r.denominator() for r in R(n, n, x).list()]
for n in (0..9): print(A362997row(n))
CROSSREFS
Cf. A362996 (numerator), A002805 (column 0), A362995.
Sequence in context: A016545 A142977 A356601 * A120108 A350292 A060556
KEYWORD
nonn,tabl,frac
AUTHOR
Peter Luschny, May 13 2023
STATUS
approved