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a(n) = (4n)!/(24^n).
24

%I #21 Jan 26 2022 03:20:41

%S 1,1,70,34650,63063000,305540235000,3246670537110000,

%T 66475579247327250000,2390461829733887910000000,

%U 140810154080474667338550000000,12868639981414579848070084500000000,1746930746117010628955362040959500000000

%N a(n) = (4n)!/(24^n).

%C a(n) is also the constant term in product 1 <= i,j <= n, i different from j (1 - x_i/x_j)^4. - Sharon Sela (sharonsela(AT)hotmail.com), Feb 16 2002

%D George E. Andrews, Richard Askey and Ranjan Roy, Special Functions, Cambridge University Press, 1998.

%H Alois P. Heinz, <a href="/A014608/b014608.txt">Table of n, a(n) for n = 0..130</a>

%H J.-C. Novelli and J.-Y. Thibon, <a href="http://arxiv.org/abs/1403.5962">Hopf Algebras of m-permutations,(m+1)-ary trees, and m-parking functions</a>, arXiv preprint arXiv:1403.5962 [math.CO], 2014-2020.

%F From _Amiram Eldar_, Jan 26 2022: (Start)

%F Sum_{n>=0} 1/a(n) = (cos(2^(3/4)*3^(1/4)) + cosh(2^(3/4)*3^(1/4)))/2.

%F Sum_{n>=0} (-1)^n/a(n) = cos(6^(1/4))*cosh(6^(1/4)). (End)

%t Table[(4n)!/24^n,{n,0,10}] (* _Harvey P. Dale_, Oct 15 2015 *)

%o (PARI) a(n)=(4*n)!/24^n;

%Y Cf. A000680, A014606.

%K nonn

%O 0,3

%A BjornE (mdeans(AT)algonet.se)