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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.

Showing 1-2 of 2 results.

A256881 a(n) = n!/ceiling(n/2).

Original entry on oeis.org

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

Views

Author

M. F. Hasler, Apr 22 2015

Keywords

Comments

Original name was: n!/round(n/2). - Robert Israel, Sep 03 2018

Links

Crossrefs

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

Programs

  • Magma
    [Factorial(n)/Round(n/2): n in [1..30]]; // Vincenzo Librandi, Apr 23 2015
  • 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 *)
  • 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).
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

Extensions

Definition clarified by Robert Israel, Sep 03 2018

A322544 a(n) is the reciprocal of the coefficient of x^n in the power series defined by ((1+2x)*exp(x) + 3*exp(-x) - 4)/ (4x^2).

Original entry on oeis.org

1, 6, 8, 60, 180, 1680, 8064, 90720, 604800, 7983360, 68428800, 1037836800, 10897286400, 186810624000, 2324754432000, 44460928512000, 640237370572800, 13516122267648000, 221172909834240000, 5109094217170944000, 93666727314800640000, 2350183339898634240000, 47726800133326110720000
Offset: 0

Views

Author

Pierre-Alain Sallard, Dec 14 2018

Keywords

Links

Crossrefs

Cf. A060593 (even bisection, shifted), A028242 (denominator minus 1), A030451 (denominator, shifted), A107991 (Expansion of a similar function), A073743.

Programs

  • GAP
    List([0..25],n->(4*Factorial(n+2))/(2*n+5+3*(-1)^n)); # Muniru A Asiru, Dec 20 2018
  • Maple
    a:=n->factorial(n+2)/(3*floor(n/2)-n+2): seq(a(n),n=0..25); # Muniru A Asiru, Dec 20 2018
  • Mathematica
    Table[4*Factorial[n + 2]/(2*n + 5 + 3*(-1)^n), {n, 0, 25}]
(* or *)
Function[x, 1/x] /@
CoefficientList[Series[(Exp[x]/4 + 3/4*Exp[-x] + x/2*Exp[x] - 1)/x^2, {x, 0, 20}], x]
  • PARI
    a(n)={(4*(n+2)!)/(5 + 3*(-1)^n + 2*n)} \\ Andrew Howroyd, Dec 14 2018
  • PARI
    my(x='x + O('x^30)); Vec(apply(x->1/x, ((1+2*x)*exp(x) + 3*exp(-x) - 4)/ (4*x^2))) \\ Michel Marcus, Dec 19 2018

Formula

a(n) = (n+2)!/(3*floor(n/2)-n+2).
a(n) = (4*(n+2)!)/(2n+5+3*(-1)^n).
a(n) = 4/([x^n]((exp(x)*(1+2x)+3*exp(-x)-4)/x^2)).
a(n) = (n+2)!/(A028242(n)+1).
a(n) = (n+2)!/A030451(n+1).
a(n) ~ sqrt(Pi/2)/72*exp(-n)*n^(n-1/2)*(1705 - 264*n + 288*n^2). - Stefano Spezia, Aug 11 2025
Sum_{n>=0} 1/a(n) = 3*cosh(1)/2 - 1. - Amiram Eldar, Aug 15 2025
Showing 1-2 of 2 results.

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