This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A309105 #10 Aug 06 2020 15:29:36
%S A309105 1,1,3,9,25,71,198,543,1486,4045,11007,29931,81371,221197,601294,
%T A309105 1634497,4443046,12077467,32829975,89241140,242582583,659407855,
%U A309105 1792456409,4872401706,13244561047,36002449653,97864804698,266024120284,723128532126,1965667148553
%N A309105 a(n) = Sum_{k >= 0} floor(n^(2*k) / (2*k)!).
%C A309105 This sequence is inspired by the Maclaurin series for the hyperbolic cosine function.
%H A309105 Wikipedia, <a href="https://en.wikipedia.org/wiki/Taylor_series#Hyperbolic_functions">Taylor series: Hyperbolic functions</a>
%F A309105 a(n) ~ cosh(n) as n tends to infinity.
%F A309105 a(n) <= A000501(n).
%e A309105 For n = 5:
%e A309105 - we have:
%e A309105 k 5^(2*k)/(2*k)!
%e A309105 -- --------------
%e A309105 0 1
%e A309105 1 12
%e A309105 2 26
%e A309105 3 21
%e A309105 4 9
%e A309105 5 2
%e A309105 6 0
%e A309105 - hence a(5) = 1 + 12 + 26 + 21 + 9 + 2 = 71.
%o A309105 (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)))) }
%Y A309105 See A309087 for similar sequences.
%Y A309105 Cf. A000501.
%K A309105 nonn
%O A309105 0,3
%A A309105 _Rémy Sigrist_, Jul 12 2019
%E A309105 Definition corrected by _Rémy Sigrist_, Aug 06 2020