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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 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.)