A129326 - OEIS

%I #39 Sep 08 2022 08:45:30

%S 3,5,14,54,264,1560,10800,85680,766080,7620480,83462400,997920000,

%T 12933043200,180583603200,2702527027200,43153254144000,

%U 732297646080000,13160434839552000,249692574523392000,4987449116762112000,104614786351595520000,2299092397726924800000

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

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

%H Vincenzo Librandi, <a href="/A129326/b129326.txt">Table of n, a(n) for n = 1..100</a>

%F a(n) = A052649(n-1), n > 1. - _R. J. Mathar_, Jun 14 2008

%F 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

%F E.g.f.: 2*x/(1-x) - log(1-x). - _G. C. Greubel_, Nov 02 2018

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

%t Table[(2n+1)(n-1)!,{n,30}] (* _Harvey P. Dale_, Mar 23 2012 *)

%o (Magma) [(2*n+1)*Factorial(n-1): n in [1..25]]; // _Vincenzo Librandi_, Aug 07 2011

%o (PARI) vector(30, n, (2*n+1)*(n-1)!) \\ _G. C. Greubel_, Nov 02 2018

%Y Cf. A052649.

%K nonn,easy

%O 1,1

%A _Paul Curtz_, May 26 2007

%E More terms from _N. J. A. Sloane_, Nov 08 2007