A002867 a(n) = binomial(n,floor(n/2))*(n+1)!. (Formerly M2035 N0806)

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

Offset

0,2

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.

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

Sum_{n>0} (n-1)!/a(n) = 1 + 4*G/3 - Pi*sqrt(3)/6 - Pi*log(2+sqrt(3))/6, where G = Catalan's constant (A006752). - Peter McNair, Oct 13 2025

Mathematica

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

Crossrefs

Cf. A000246.

Sequence in context: A335786 A005443 A362796 * A235359 A130426 A002397

Adjacent sequences: A002864 A002865 A002866 * A002868 A002869 A002870

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from James Sellers, Jul 10 2000

Status

approved