A226730 - OEIS

%I #18 Sep 08 2022 08:46:05

%S 2,8,66,864,15240,333360,8653680,259499520,8821975680,335224915200,

%T 14079333945600,647648004326400,32382382493260800,1748648405555251200,

%U 101421603773538048000,6288139373806338048000,415017197646001606656000,29051203816724366204928000

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

%C The product of the first parts of the partitions of 2n into exactly two parts plus the product of the second parts of the partitions of 2n into exactly two parts.

%H Vincenzo Librandi, <a href="/A226730/b226730.txt">Table of n, a(n) for n = 1..370</a>

%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>

%F a(n) = n! + (2n-1)!/(n-1)!.

%F E.g.f.: 1/(1 - x) + 1/(2*sqrt(1 - 4*x)) - 3/2. - _Ilya Gutkovskiy_, Dec 06 2016

%e a(3) = 66, since 2(3) = 6 has 3 partitions with exactly two parts: (5,1), (4,2), and (3,3).  a(3) = 5*4*3 + 1*2*3 = 60 + 6 = 66.

%t Table[n! + (2 n - 1)! / (n - 1)!, {n, 20}] (* _Vincenzo Librandi_, Feb 07 2018 *)

%o (Magma) [Factorial(n)+Factorial(2*n-1) div Factorial(n-1): n in [1..20]]; // _Vincenzo Librandi_, Feb 07 2018

%K nonn,easy

%O 1,1

%A _Wesley Ivan Hurt_, Jun 15 2013