A002867 a(n) = binomial(n,floor(n/2))*(n+1)!.

1, 2, 12, 72, 720, 7200, 100800, 1411200, 25401600, 457228800, 10059033600, 221298739200, 5753767219200, 149597947699200, 4487938430976000, 134638152929280000, 4577697199595520000, 155641704786247680000, 5914384781877411840000, 224746621711341649920000

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

References

• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• T. D. Noe, Table of n, a(n) for n = 0..100
• Victor Meally, Comparison of several sequences given in Motzkin's paper "Sorting numbers for cylinders...", letter to N. J. A. Sloane, N. D.
• Theodore S. Motzkin, Sorting numbers for cylinders and other classification numbers, in Combinatorics, Proc. Symp. Pure Math. 19, AMS, 1971, pp. 167-176. [Annotated, scanned copy]
• OEIS Wiki, Sorting numbers.

Crossrefs

Cf. A000246.

Programs

Mathematica

Table[Binomial[n,Floor[n/2]](n+1)!,{n,0,20}] (* Harvey P. Dale, Sep 04 2018 *)

Formula

a(n) = 2^n * A000246(n+1).

E.g.f.: 1/(sqrt(1+2*x)*(1-2*x)^(3/2)) = 1/(sqrt(1-4*x^2)*(1-2*x)). - Paul Barry, Jul 22 2005

Conjecture: a(n) - 2*a(n-1) - 4*n*(n-1)*a(n-2) = 0. - R. J. Mathar, Nov 24 2012

Sum_{n>=0} 1/a(n) = (StruveL(-1,1/2) + StruveL(0,1/2))*Pi/2, where StruveL is the modified Struve function. - Amiram Eldar, Aug 15 2025

Extensions

More terms from James Sellers, Jul 10 2000