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Search: id:A102189
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| A102189 |
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Array of multinomial numbers (row reversed order of table A036039.). |
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+0
5
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| 1, 1, 1, 1, 3, 2, 1, 6, 3, 8, 6, 1, 10, 15, 20, 20, 30, 24, 1, 15, 45, 40, 15, 120, 90, 40, 90, 144, 120, 1, 21, 105, 70, 105, 420, 210, 210, 280, 630, 504, 420, 504, 840, 720, 1, 28, 210, 112, 420, 1120, 420, 105, 1680, 1120, 2520, 1344, 1120, 1260, 3360, 4032, 3360
(list; graph; listen)
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OFFSET
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1,5
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COMMENT
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See Abramowitz and Stegun, Handbook, p. 831, column labeled "M_2", read backwards.
The sequence of row lengths is [1,2,3,5,7,11,15,...]=A000041(n), n>=1, (partition numbers).
Row n of this array gives the coefficients of the cycle index polynomial n!*Z(S_n) for the symmetric group S_n. For instance, Z(S_4)= (x[1]^4 + 6*x[1]^2*x[2] + 3*x[2]^2 + 8*x[1]*x[3] + 6*x[4])/4!. The partitions of 4 appear here in the reversed Abramowitz-Stegun order.
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LINKS
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, December 1972 [alternative scanned copy].
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, December 1972, pp. 831-2.
W. Lang, More rows and S_n cycle index polynomials.
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EXAMPLE
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[1];[1,1];[1,3,2];[1,6,3,8,6];[1,10,15,20,20,30,24];...
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CROSSREFS
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Sequence in context: A002130 A089145 A134199 this_sequence A031252 A129674 A120771
Adjacent sequences: A102186 A102187 A102188 this_sequence A102190 A102191 A102192
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KEYWORD
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nonn,easy,tabf
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Feb 15 2005
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