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A372311
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Triangle read by rows: T(n, k) = n^k * Sum_{j=0..n} binomial(n - j, n - k) * Eulerian1(n, j).
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1
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1, 1, 1, 1, 6, 8, 1, 21, 108, 162, 1, 60, 800, 3840, 6144, 1, 155, 4500, 48750, 225000, 375000, 1, 378, 21672, 453600, 4354560, 19595520, 33592320, 1, 889, 94668, 3500658, 60505200, 536479440, 2371803840, 4150656720
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table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,5
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LINKS
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EXAMPLE
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Triangle begins:
[0] 1;
[1] 1, 1;
[2] 1, 6, 8;
[3] 1, 21, 108, 162;
[4] 1, 60, 800, 3840, 6144;
[5] 1, 155, 4500, 48750, 225000, 375000;
[6] 1, 378, 21672, 453600, 4354560, 19595520, 33592320;
[7] 1, 889, 94668, 3500658, 60505200, 536479440, 2371803840, 4150656720;
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MAPLE
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S := (n, k) -> local j; add(eulerian1(n, j)*binomial(n-j, n-k), j = 0..n):
row := n -> local k; seq(S(n, k) * n^k, k = 0..n):
seq(row(n), n = 0..8);
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PROG
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(SageMath)
x = polygen(ZZ, 'x')
A = []
for m in range(0, n + 1, 1) :
A.append((-x)^m)
for j in range(m, 0, -1):
A[j - 1] = j * (A[j - 1] - A[j])
return [n^k*c for k, c in enumerate(A[0])]
for n in (0..7) : print(A372311_row(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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