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A052127 Sum a(n) x^n / n!^2 = exp(-2x)/(1-x)^3. 3


%S 1,1,8,96,2112,68160,3087360,185633280,14301020160,1372232171520,

%T 160390869811200,22426206024499200,3695148753459609600,

%U 708443854690399027200,156340439420689081958400,39342248735234589720576000,11197266840049016358567936000

%N Sum a(n) x^n / n!^2 = exp(-2x)/(1-x)^3.

%C 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

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

%D 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).

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

%Y Cf. A052124.

%K nonn

%O 0,3

%A _N. J. A. Sloane_, Jan 23 2000

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Last modified September 29 04:42 EDT 2020. Contains 337420 sequences. (Running on oeis4.)