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

1,2

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).

a(2n+1) = A110468(n) = A107991(2n+2) = A229244(2n+1), n>=0.

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

Cf. A009445, A052612, A052616, A052849, A081457, A208529, A098558, A107991, A110468, A229244, A256031.

Sequence in context: A151368 A087650 A177699 * A012514 A012511 A012309

Adjacent sequences: A256878 A256879 A256880 * A256882 A256883 A256884

Keyword

nonn

Author

M. F. Hasler, Apr 22 2015

Extensions

Definition clarified by Robert Israel, Sep 03 2018

Status

approved