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Search: id:A124303
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| A124303 |
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Number of set partitions of length <=4; sum of first 4 columns of triangle of Stirling numbers of 2nd kind; dimension of space of symmetric polynomials in 4 noncommuting variables. |
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+0
3
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| 1, 1, 2, 5, 15, 51, 187, 715, 2795, 11051, 43947, 175275, 700075, 2798251, 11188907, 44747435, 178973355, 715860651, 2863377067, 11453377195, 45813246635, 183252462251, 733008800427, 2932033104555, 11728128223915, 46912504507051
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Apart from initial term, same as A007581. - Valery A. Liskovets (liskov(AT)im.bas-net.by), Nov 16 2006
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REFERENCES
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N. Bergeron, C. Reutenauer, M. Rosas, M. Zabrocki, Invariants and Coinvariants of the Symmetric Group in Noncommuting Variables, to appear Canad. J. Math., arXiv: math.CO/0502082
M. Rosas and B. Sagan, Symmetric Functions in Noncommuting Variables. Transactions of the American Mathematical Society, 358 (2006), no. 1, 215-232.
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FORMULA
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O.g.f. (3*q^3 - 9*q^2 + 6*q - 1)/(8*q^3 - 14*q^2 + 7*q - 1) = sum(q^k/prod((1-i*q),i=1..k),k=0..4) a(n) = 7*a(n-1)-14*a(n-2)+8*a(n-3); a(0) = 1, a(1) = 1, a(2) = 2, a(3) = 5 a(n) = add(A008277(n,k),k=1..4)
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EXAMPLE
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Number of set partitions of {1,2,3,4,5,6} are given by A008277(6,k) = 1, 31, 90, 65, 15, 1 and hence a(6) = 1+31+90+65 = 187
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MAPLE
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a:=proc(n); if n<4 then [1, 1, 2, 5][n+1]; else 7*a(n-1)-14*a(n-2)+8*a(n-3); fi; end:
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CROSSREFS
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Cf. A124292, A000110, A008277.
Adjacent sequences: A124300 A124301 A124302 this_sequence A124304 A124305 A124306
Sequence in context: A060049 A107590 A007581 this_sequence A073525 A007317 A132018
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KEYWORD
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nonn
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AUTHOR
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Mike Zabrocki (zabrocki(AT)mathstat.yorku.ca), Oct 25 2006
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