OFFSET
0,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..123
FORMULA
Limit_{n->infinity} a(n)^(1/n^2) = ((1-r)/r)^(r^2/(4*r-1)) = 1.17123387669321050316385592324128471190583619526359450226558587879190245..., where r = A323773 = 0.3663201503052830964087236563781171194011826607210994595... is the root of the equation (1-2*r)^(4*r-1) * (1-r)^(1-2*r) = r^(2*r).
MATHEMATICA
Table[Sum[Binomial[n-k, k]^k, {k, 0, n/2}], {n, 0, 25}]
PROG
(PARI) {a(n) = sum(k=0, n\2, binomial(n-k, k)^k)} \\ Seiichi Manyama, Jan 27 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Jan 27 2019
STATUS
approved