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A156815
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Triangle T(n, k) = n!*StirlingS2(n, k)/binomial(n, k), read by rows.
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1
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1, 0, 1, 0, 1, 2, 0, 2, 6, 6, 0, 6, 28, 36, 24, 0, 24, 180, 300, 240, 120, 0, 120, 1488, 3240, 3120, 1800, 720, 0, 720, 15120, 43344, 50400, 33600, 15120, 5040, 0, 5040, 182880, 695520, 979776, 756000, 383040, 141120, 40320, 0, 40320, 2570400, 13068000, 22377600, 20018880, 11430720, 4656960, 1451520, 362880
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,6
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REFERENCES
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Steve Roman, The Umbral Calculus, Dover Publications, New York (1984), page 99.
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LINKS
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G. C. Greubel, Rows n = 0..50 of the triangle, flattened
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FORMULA
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T(n, k) = n!*StirlingS2(n, k)/binomial(n, k).
From G. C. Greubel, Jun 10 2021: (Start)
T(n, 1) = T(n, n) = n!.
T(n, 2) = 2*A029767(n+1).
T(n, n-1) = A180119(n). (End)
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EXAMPLE
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Triangle begins as:
1;
0, 1;
0, 1, 2;
0, 2, 6, 6;
0, 6, 28, 36, 24;
0, 24, 180, 300, 240, 120;
0, 120, 1488, 3240, 3120, 1800, 720;
0, 720, 15120, 43344, 50400, 33600, 15120, 5040;
0, 5040, 182880, 695520, 979776, 756000, 383040, 141120, 40320;
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MATHEMATICA
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T[n_, k_] = n!*StirlingS2[n, k]/Binomial[n, k];
Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten
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PROG
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(Magma) [Factorial(n)*StirlingSecond(n, k)/Binomial(n, k): k in [0..n], n in [0..12]]; // G. C. Greubel, Jun 10 2021
(Sage) flatten([[factorial(n)*stirling_number2(n, k)/binomial(n, k) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Jun 10 2021
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CROSSREFS
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Cf. A048993, A029767, A180119.
Sequence in context: A291799 A295027 A225479 * A303439 A303345 A175802
Adjacent sequences: A156812 A156813 A156814 * A156816 A156817 A156818
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KEYWORD
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nonn,tabl
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AUTHOR
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Roger L. Bagula, Feb 16 2009
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EXTENSIONS
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Edited by G. C. Greubel, Jun 10 2021
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STATUS
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approved
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