OFFSET
0,3
COMMENTS
This sequence is inspired by the Maclaurin series for the hyperbolic cosine function.
LINKS
FORMULA
a(n) ~ cosh(n) as n tends to infinity.
a(n) <= A000501(n).
EXAMPLE
For n = 5:
- we have:
k 5^(2*k)/(2*k)!
-- --------------
0 1
1 12
2 26
3 21
4 9
5 2
6 0
- hence a(5) = 1 + 12 + 26 + 21 + 9 + 2 = 71.
PROG
(PARI) a(n) = { my (v=0, d=1); forstep (k=1, oo, 2, if (d<1, return (v), v += floor(d); d *= n^2/(k*(k+1)))) }
CROSSREFS
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Jul 12 2019
EXTENSIONS
Definition corrected by Rémy Sigrist, Aug 06 2020
STATUS
approved