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A309105
a(n) = Sum_{k >= 0} floor(n^(2*k) / (2*k)!).
1
1, 1, 3, 9, 25, 71, 198, 543, 1486, 4045, 11007, 29931, 81371, 221197, 601294, 1634497, 4443046, 12077467, 32829975, 89241140, 242582583, 659407855, 1792456409, 4872401706, 13244561047, 36002449653, 97864804698, 266024120284, 723128532126, 1965667148553
OFFSET
0,3
COMMENTS
This sequence is inspired by the Maclaurin series for the hyperbolic cosine function.
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
See A309087 for similar sequences.
Cf. A000501.
Sequence in context: A333608 A058719 A046661 * A101197 A233828 A101168
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Jul 12 2019
EXTENSIONS
Definition corrected by Rémy Sigrist, Aug 06 2020
STATUS
approved