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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

This sequence is inspired by the Maclaurin series for the hyperbolic cosine function.

LINKS

Table of n, a(n) for n=0..29.

Wikipedia, Taylor series: Hyperbolic functions

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

Adjacent sequences:  A309102 A309103 A309104 * A309106 A309107 A309108

KEYWORD

nonn

AUTHOR

Rémy Sigrist, Jul 12 2019

EXTENSIONS

Definition corrected by Rémy Sigrist, Aug 06 2020

STATUS

approved

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Last modified October 1 04:06 EDT 2020. Contains 337441 sequences. (Running on oeis4.)