

A328716


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


2



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

0,3


COMMENTS

a(n) is the number of nstep closed walks (from origin to origin) in ndimensional 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)


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


CROSSREFS

Main diagonal of A328718.
Sequence in context: A135171 A058765 A317340 * A067967 A092751 A122150
Adjacent sequences: A328713 A328714 A328715 * A328717 A328718 A328719


KEYWORD

nonn


AUTHOR

Seiichi Manyama, Oct 26 2019


EXTENSIONS

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


STATUS

approved



