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1, 2, 1, 5, 4, 1, 15, 14, 7, 1, 52, 51, 36, 11, 1, 203, 202, 171, 81, 16, 1, 877, 876, 813, 512, 162, 22, 1, 4140, 4139, 4012, 3046, 1345, 295, 29, 1, 21147, 21146, 20891, 17866, 10096, 3145, 499, 37, 1, 115975, 115974, 115463
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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Left column = Bell numbers (A000110) starting (1, 2, 5, 15, 52, 203, ...). Row sums = A005493(n+1): (1, 3, 10, 37, 151, 674, ...).
Corresponding to the generalized Stirling number triangle of first kind A049444. - Peter Luschny, Sep 18 2011
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LINKS
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FORMULA
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A008277 * A000012 as infinite lower triangular matrices. Partial sums of A008277 rows starting from the right.
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EXAMPLE
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First few rows of the triangle are
1;
2, 1;
5, 4, 1;
15, 14, 7, 1;
52, 51, 36, 11, 1;
203, 202, 171, 81, 16, 1;
877, 876, 813, 512, 162, 22, 1;
...
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MAPLE
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add(add(combinat[stirling2](n, n-i), i=0..k)*x^(n-k-1), k=0..n-1);
seq(coeff(%, x, k), k=0..n-1) end:
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MATHEMATICA
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row[n_] := Table[StirlingS2[n, k], {k, 0, n}] // Reverse // Accumulate // Reverse // Rest;
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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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