A226730 a(n) = n! + (2*n-1)!/(n-1)!.

2, 8, 66, 864, 15240, 333360, 8653680, 259499520, 8821975680, 335224915200, 14079333945600, 647648004326400, 32382382493260800, 1748648405555251200, 101421603773538048000, 6288139373806338048000, 415017197646001606656000, 29051203816724366204928000

Offset

1,1

Comments

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.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..370

Index entries for sequences related to partitions

Formula

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

E.g.f.: 1/(1 - x) + 1/(2*sqrt(1 - 4*x)) - 3/2. - Ilya Gutkovskiy, Dec 06 2016

Example

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.

Mathematica

Table[n! + (2 n - 1)! / (n - 1)!, {n, 20}] (* Vincenzo Librandi, Feb 07 2018 *)

Prog

(Magma) [Factorial(n)+Factorial(2*n-1) div Factorial(n-1): n in [1..20]]; // Vincenzo Librandi, Feb 07 2018

Crossrefs

Sequence in context: A231280 A086594 A132219 * A202553 A023164 A053922

Adjacent sequences: A226727 A226728 A226729 * A226731 A226732 A226733

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Jun 15 2013

Status

approved