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A371076
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Triangle read by rows: T(n, k) = 3^n*Sum_{j=0..k} (-1)^(k - j)*binomial(k, j) * Pochhammer(j/3, n).
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3
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1, 0, 1, 0, 4, 2, 0, 28, 24, 6, 0, 280, 320, 144, 24, 0, 3640, 5040, 3120, 960, 120, 0, 58240, 92960, 71280, 30720, 7200, 720, 0, 1106560, 1975680, 1775760, 960960, 319200, 60480, 5040, 0, 24344320, 47653760, 48545280, 31127040, 13104000, 3548160, 564480, 40320
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OFFSET
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0,5
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LINKS
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FORMULA
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T(n, k) = k * T(n-1, k-1) + (3*n - 3 + k) * T(n-1, k) for 0 < k < n with initial values T(n, 0) = 0 for n > 0 and T(n, n) = n! for n >= 0. - Werner Schulte, Mar 13 2024
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EXAMPLE
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Triangle starts:
[0] 1;
[1] 0, 1;
[2] 0, 4, 2;
[3] 0, 28, 24, 6;
[4] 0, 280, 320, 144, 24;
[5] 0, 3640, 5040, 3120, 960, 120;
[6] 0, 58240, 92960, 71280, 30720, 7200, 720;
[7] 0, 1106560, 1975680, 1775760, 960960, 319200, 60480, 5040;
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MAPLE
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A371076 := (n, k) -> local j; 3^n*add((-1)^(k - j)*binomial(k, j)*pochhammer(j/3, n), j = 0..k): seq(seq(A371076(n, k), k = 0..n), n = 0..9);
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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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