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A052127 Sum a(n) x^n / n!^2 = exp(-2x)/(1-x)^3. 3
1, 1, 8, 96, 2112, 68160, 3087360, 185633280, 14301020160, 1372232171520, 160390869811200, 22426206024499200, 3695148753459609600, 708443854690399027200, 156340439420689081958400, 39342248735234589720576000, 11197266840049016358567936000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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

REFERENCES

R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.64(b).

Szekeres, G. The average value of skew Hadamard matrices. Proceedings of the First Australian Conference on Combinatorial Mathematics (Univ. Newcastle, Newcastle, 1972), pp. 55--59. Univ. of Newcastle Res. Associates, Newcastle, 1972. MR0349708 (50 #2201). This is S_4(n).

LINKS

Table of n, a(n) for n=0..16.

FORMULA

a(n) = (n!)^2*A209429(n)/A209430(n). [Szekeres]

CROSSREFS

Cf. A052124.

Sequence in context: A002168 A114425 A224767 * A002506 A218451 A262777

Adjacent sequences:  A052124 A052125 A052126 * A052128 A052129 A052130

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jan 23 2000

STATUS

approved

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Last modified February 24 22:41 EST 2018. Contains 299627 sequences. (Running on oeis4.)