A328716 Constant term in the expansion of (1 + x_1 + x_2 + ... + x_n + 1/x_1 + 1/x_2 + ... + 1/x_n)^n.

1, 1, 5, 19, 217, 1451, 26041, 249705, 6116209, 76432627, 2373097921, 36562658573, 1374991573825, 25188442156333, 1112491608614933, 23620069750701091, 1198207214200181217, 28930659427538020915, 1657461085278025906081, 44848606508761385855085

Offset: 0

Author

Seiichi Manyama, Oct 26 2019

Keywords

• nonn

Comments

a(n) is the number of n-step closed walks (from origin to origin) in n-dimensional lattice where each step changes at most one component by -1 or by +1. - Alois P. Heinz, Oct 26 2019

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..398 (terms 0..199 from Alois P. Heinz)

Crossrefs

Main diagonal of A328718.

Formula

a(n) = n! * [x^n] exp(x) * BesselI(0,2*x)^n. - Ilya Gutkovskiy, Oct 26 2019

a(n) ~ c * d^n * n^n, where d = 0.8047104059195202206625458331930618795... and c = 2.12946224998808159475495497... if n is even and c = 1.4189559976544232606562785... if n is odd. - Vaclav Kotesovec, Oct 27 2019

Extensions

a(7)-a(19) from Alois P. Heinz, Oct 26 2019