A014608 a(n) = (4n)!/(24^n).

1, 1, 70, 34650, 63063000, 305540235000, 3246670537110000, 66475579247327250000, 2390461829733887910000000, 140810154080474667338550000000, 12868639981414579848070084500000000, 1746930746117010628955362040959500000000

Offset: 0

Author

BjornE (mdeans(AT)algonet.se)

Keywords

• nonn

Comments

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

References

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

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..130
• J.-C. Novelli and J.-Y. Thibon, Hopf Algebras of m-permutations,(m+1)-ary trees, and m-parking functions, arXiv preprint arXiv:1403.5962 [math.CO], 2014-2020.

Crossrefs

Cf. A000680, A014606.

Programs

Mathematica

Table[(4n)!/24^n,{n,0,10}] (* Harvey P. Dale, Oct 15 2015 *)

PARI

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

Formula

From Amiram Eldar, Jan 26 2022: (Start)

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

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