A055660 Number of (2,2; n,n)-partitions of a chain of length n^2 + n.

15, 168, 1260, 7920, 45045, 240240, 1225224, 6046560, 29099070, 137287920, 637408200, 2920488480, 13233463425, 59400885600, 264475371600, 1169259537600, 5137434093330, 22449291836400, 97620405409800, 422649444016800, 1822675727322450, 7832297982551328, 33547430170018800

Offset

4,1

Comments

The sequence {a(n)/3} is A030060 a (k_1,n_1; k_2,n_2)-partition of a chain C is a chain of k_1+k_2 intervals of C, k_1 being of length n_1 and k_2 of length n_2.

Links

Vincenzo Librandi, Table of n, a(n) for n = 4..200

Formula

a(n) = 2*(2*n-3)*(n-3)*(2*n-5)!/((n-3)!^2*n).

From Amiram Eldar, Mar 22 2022: (Start)

Sum_{n>=4} 1/a(n) = Pi/(2*sqrt(3)) - 5/6.

Sum_{n>=4} (-1)^n/a(n) = 3*sqrt(5)*log(phi) - 19/6, where phi is the golden ratio (A001622). (End)

Example

a(4)=15 because in the linearly ordered set {1,..,20} we can choose in 15 ways 6 successive blocks, 2 constituted of 2 consecutive elements and 4 of 4 consecutive elements.

Mathematica

Table[2*(2*n - 3)*(n - 3)*(2*n - 5)!/((n - 3)!^2*n), {n, 4, 25}] (* Amiram Eldar, Mar 22 2022 *)

Prog

(Magma) [Factorial(2*n-5)*2*(2*n-3)*(n-3)/Factorial(n-3)^2/n: n in [4..25]]; // Vincenzo Librandi, Jun 30 2011

Crossrefs

Cf. A001622, A030060, A055663.

Sequence in context: A210326 A016234 A160197 * A121114 A121116 A218928

Adjacent sequences: A055657 A055658 A055659 * A055661 A055662 A055663

Keyword

nonn

Author

Paolo Dominici (pl.dm(AT)libero.it), Jun 07 2000

Status

approved