A256881 a(n) = n!/ceiling(n/2).
1, 2, 3, 12, 40, 240, 1260, 10080, 72576, 725760, 6652800, 79833600, 889574400, 12454041600, 163459296000, 2615348736000, 39520825344000, 711374856192000, 12164510040883200, 243290200817664000, 4644631106519040000, 102181884343418880000, 2154334728240414720000
Offset: 1
Keywords
Links
- Robert Israel, Table of n, a(n) for n = 1..450
- Pierre-Alain Sallard, Sum of repeated integrals of sinh.
Crossrefs
Programs
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Magma
[Factorial(n)/Round(n/2): n in [1..30]]; // Vincenzo Librandi, Apr 23 2015
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Maple
A256881 := n!/round(n/2);
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Mathematica
Function[x, 1/x] /@ CoefficientList[Series[(Sinh[x] + x*Exp[x])/2, {x, 0, 20}], x] (* Pierre-Alain Sallard, Dec 15 2018 *) -
PARI
A256881(n)=n!/round(n/2)
Formula
a(2n) = 2*A009445(n) = A052612(2n-1) = A052616(2n-1) = A052849(2n-1) = A098558(2n-1) = A081457(3n-1) = A208529(2n+1) = A256031(2n-1).
From Robert Israel, Sep 03 2018: (Start)
E.g.f.: -(1+1/x)*log(1-x^2).
n*(n+1)*(n+2)*a(n)+(n+2)*a(n+1)-(n+3)*a(n+2)=0. (End)
a(n) = 2/([x^n](sinh(x) + x*exp(x))). - Pierre-Alain Sallard, Dec 15 2018
Sum_{n>=1} 1/a(n) = (3*e-1/e)/4 = (e + sinh(1))/2. - Amiram Eldar, Feb 02 2023
Extensions
Definition clarified by Robert Israel, Sep 03 2018
Comments