OFFSET
1,2
COMMENTS
Original name was: n!/round(n/2). - Robert Israel, Sep 03 2018
LINKS
Robert Israel, Table of n, a(n) for n = 1..450
Pierre-Alain Sallard, Sum of repeated integrals of sinh.
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
MAPLE
A256881 := n!/round(n/2);
MATHEMATICA
Function[x, 1/x] /@
CoefficientList[Series[(Sinh[x] + x*Exp[x])/2, {x, 0, 20}], x] (* Pierre-Alain Sallard, Dec 15 2018 *)
PROG
(PARI) A256881(n)=n!/round(n/2)
(Magma) [Factorial(n)/Round(n/2): n in [1..30]]; // Vincenzo Librandi, Apr 23 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
M. F. Hasler, Apr 22 2015
EXTENSIONS
Definition clarified by Robert Israel, Sep 03 2018
STATUS
approved