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A052127
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Sum a(n) x^n / n!^2 = exp(-2x)/(1-x)^3.
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1
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1, 1, 8, 96, 2112, 68160, 3087360, 185633280, 14301020160, 1372232171520, 160390869811200, 22426206024499200, 3695148753459609600, 708443854690399027200, 156340439420689081958400, 39342248735234589720576000, 11197266840049016358567936000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| As described in the Stanley reference, this sequence gives the expectation of the fourth moment of a random sign matrix (a matrix whose entries are independently set equal to -1 or 1 with equal probability) of size n. For large n, a(n) asymptotic to (n!)^2 (n^2+7n+10)/(2e^2) . - Kevin P. Costello (kcostell(AT)gmail.com), Oct 22 2007
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REFERENCES
| R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.64(b).
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CROSSREFS
| Cf. A052124.
Sequence in context: A052570 A002168 A114425 * A002506 A083182 A116267
Adjacent sequences: A052124 A052125 A052126 * A052128 A052129 A052130
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jan 23 2000
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