OFFSET
0,3
COMMENTS
Also number of n-step closed walks (from origin to origin) in n-dimensional lattice, using steps (t_1,t_2, ... ,t_n) (t_k = -1, 1 or 0 for 1 <= k <= n) except for (0,0, ... ,0) (t_k = 0 for 1 <= k <= n).
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..47
FORMULA
a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * A002426(k)^n.
a(n) ~ 3^(n^2 + n/2) / (exp(3/16) * 2^n * Pi^(n/2) * n^(n/2)). - Vaclav Kotesovec, Oct 30 2019
MATHEMATICA
Table[Sum[(-1)^(n-k) * Binomial[n, k] * Sum[Binomial[k, 2*j]*Binomial[2*j, j], {j, 0, k}]^n, {k, 0, n}], {n, 0, 12}] (* Vaclav Kotesovec, Oct 30 2019 *)
PROG
(PARI) {a(n) = sum(k=0, n, (-1)^(n-k)*binomial(n, k)*polcoef((1+x+1/x)^k, 0)^n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Oct 29 2019
STATUS
approved