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Search: id:A111577
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| A111577 |
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Analogue to Stirling number of the 2nd kind triangle, read by rows. |
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+0
4
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| 1, 1, 1, 1, 5, 1, 1, 21, 12, 1, 1, 85, 105, 22, 1, 1, 341, 820, 325, 35, 1, 1, 1365, 6081, 4070, 780, 51, 1
(list; table; graph; listen)
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OFFSET
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1,5
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COMMENT
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In triangles of analogues to Stirling numbers of the second kind, multipliers of T(n-1,k) are terms in arithmetic sequences: Pascal's triangle, the multiplier = 1. Stirling number of the second kind triangle A008277, the multipliers are in the set (1,2,3...); and in the analogue A039755, the multipliers are in the sequence (1,3,5...). The multipliers in A111577 are terms of 3k-2(k>0): 1,4,7,10,... First few rows of the triangle are: 1; 1, 1; 1, 5, 1; 1, 21, 12, 1; 1, 85, 105, 22, 1;
Riordan array [exp(x), (exp(3x)-1)/3]. [From Paul Barry (pbarry(AT)wit.ie), Nov 26 2008]
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REFERENCES
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R. Suter, Two Analogues of a Classical Sequence, Journal of Integer Sequences, Article 00.1.8 [From Paul Barry (pbarry(AT)wit.ie), Nov 26 2008]
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FORMULA
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T(n, k) = T(n-1, k-1) + (3k-2)*T(n-1, k).
E.g.f.: exp(x)*exp((y/3)*(exp(3x)-1)); [From Paul Barry (pbarry(AT)wit.ie), Nov 26 2008]
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EXAMPLE
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a(13) = 105 = T(5,3) = (7)(12) + 21.
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CROSSREFS
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Cf. A008277, A039755.
Sequence in context: A029847 A144397 A047909 this_sequence A036969 A080249 A022168
Adjacent sequences: A111574 A111575 A111576 this_sequence A111578 A111579 A111580
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KEYWORD
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nonn,tabl,uned,new
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 07 2005
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