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A362585
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Triangle read by rows, T(n, k) = A000670(n) * binomial(n, k).
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3
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1, 1, 1, 3, 6, 3, 13, 39, 39, 13, 75, 300, 450, 300, 75, 541, 2705, 5410, 5410, 2705, 541, 4683, 28098, 70245, 93660, 70245, 28098, 4683, 47293, 331051, 993153, 1655255, 1655255, 993153, 331051, 47293, 545835, 4366680, 15283380, 30566760, 38208450, 30566760, 15283380, 4366680, 545835
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,4
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LINKS
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EXAMPLE
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[0] 1;
[1] 1, 1;
[2] 3, 6, 3;
[3] 13, 39, 39, 13;
[4] 75, 300, 450, 300, 75;
[5] 541, 2705, 5410, 5410, 2705, 541;
[6] 4683, 28098, 70245, 93660, 70245, 28098, 4683;
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PROG
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(SageMath)
def TransOrdPart(m, n) -> list[int]:
@cached_function
def P(m: int, n: int):
R = PolynomialRing(ZZ, "x")
if n == 0: return R(1)
return R(sum(binomial(m * n, m * k) * P(m, n - k) * x
for k in range(1, n + 1)))
T = P(m, n)
def C(k) -> int:
return sum(T[j] * binomial(n, k) for j in range(n + 1))
return [C(k) for k in range(n+1)]
def A362585(n) -> list[int]: return TransOrdPart(1, n)
for n in range(6): print(A362585(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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