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A155744
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Triangle T(n, k) = (-1)^(n-k)*StirlingS1(n, k) + (-1)^k*StirlingS1(n, n-k) + (-1)^n*StirlingS1(n, k)*StirlingS1(n, n-k), read by rows.
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1
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3, 1, 1, 1, 3, 1, 1, 11, 11, 1, 1, 48, 143, 48, 1, 1, 274, 1835, 1835, 274, 1, 1, 1935, 23649, 51075, 23649, 1935, 1, 1, 15861, 310639, 1195999, 1195999, 310639, 15861, 1, 1, 146188, 4221286, 25753812, 45832899, 25753812, 4221286, 146188, 1, 1, 1491876, 59942994, 535933124, 1510548249, 1510548249, 535933124, 59942994, 1491876, 1
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OFFSET
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0,1
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LINKS
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FORMULA
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T(n, k) = (-1)^(n-k)*StirlingS1(n, k) + (-1)^k*StirlingS1(n, n-k) + (-1)^n*StirlingS1(n, k)*StirlingS1(n, n-k).
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EXAMPLE
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3;
1, 1;
1, 3, 1;
1, 11, 11, 1;
1, 48, 143, 48, 1;
1, 274, 1835, 1835, 274, 1;
1, 1935, 23649, 51075, 23649, 1935, 1;
1, 15861, 310639, 1195999, 1195999, 310639, 15861, 1;
1, 146188, 4221286, 25753812, 45832899, 25753812, 4221286, 146188, 1;
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MATHEMATICA
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T[n_, k_] = (-1)^(n-k)*StirlingS1[n, k] + (-1)^k*StirlingS1[n, n-k] + (-1)^n*StirlingS1[n, k]*StirlingS1[n, n-k];
Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten (* modified by G. C. Greubel, Jun 05 2021 *)
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PROG
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(Magma)
A155744:= func< n, k | (-1)^n*StirlingFirst(n, k)*StirlingFirst(n, n-k) + (-1)^k*StirlingFirst(n, n-k) + (-1)^(n-k)*StirlingFirst(n, k) >;
(Sage)
def A155744(n, k): return stirling_number1(n, k)*stirling_number1(n, n-k) + stirling_number1(n, k) + stirling_number1(n, n-k)
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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