A129326 a(n) = (2*n+1)*(n-1)!.

3, 5, 14, 54, 264, 1560, 10800, 85680, 766080, 7620480, 83462400, 997920000, 12933043200, 180583603200, 2702527027200, 43153254144000, 732297646080000, 13160434839552000, 249692574523392000, 4987449116762112000, 104614786351595520000, 2299092397726924800000

Offset: 1

Author

Paul Curtz, May 26 2007

Keywords

• nonn
• easy

Comments

a(n) = A052649(n-1), n > 1 (i.e., A052649 with a(0) omitted).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A052649.

Programs

Magma

[(2*n+1)*Factorial(n-1): n in [1..25]]; // Vincenzo Librandi, Aug 07 2011

Mathematica

Table[(2n+1)(n-1)!,{n,30}] (* Harvey P. Dale, Mar 23 2012 *)

PARI

vector(30, n, (2*n+1)*(n-1)!) \\ G. C. Greubel, Nov 02 2018

Formula

a(n) = A052649(n-1), n > 1. - R. J. Mathar, Jun 14 2008

a(n) = (n+1)!*h(n+1) - n*(n+1)*(n-1)!*h(n-1), where h(n) = Sum_{k=1..n} 1/k. - Gary Detlefs, Jul 19 2011

E.g.f.: 2*x/(1-x) - log(1-x). - G. C. Greubel, Nov 02 2018

Sum_{n>=1} 1/a(n) = e/2 - sqrt(Pi)*erfi(1)/4. - Amiram Eldar, Oct 07 2020

Extensions

More terms from N. J. A. Sloane, Nov 08 2007