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A362997
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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).
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2
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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
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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LINKS
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FORMULA
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EXAMPLE
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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;
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PROG
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(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))
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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