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

%I A002867 M2035 N0806 #51 Aug 15 2025 09:10:23
%S A002867 1,2,12,72,720,7200,100800,1411200,25401600,457228800,10059033600,
%T A002867 221298739200,5753767219200,149597947699200,4487938430976000,
%U A002867 134638152929280000,4577697199595520000,155641704786247680000,5914384781877411840000,224746621711341649920000
%N A002867 a(n) = binomial(n,floor(n/2))*(n+1)!.
%D A002867 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A002867 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A002867 T. D. Noe, <a href="/A002867/b002867.txt">Table of n, a(n) for n = 0..100</a>
%H A002867 Victor Meally, <a href="/A002868/a002868.pdf">Comparison of several sequences given in Motzkin's paper "Sorting numbers for cylinders...", letter to N. J. A. Sloane, N. D.</a>
%H A002867 Theodore S. Motzkin, <a href="/A000262/a000262.pdf">Sorting numbers for cylinders and other classification numbers</a>, in Combinatorics, Proc. Symp. Pure Math. 19, AMS, 1971, pp. 167-176. [Annotated, scanned copy]
%H A002867 OEIS Wiki, <a href="http://oeis.org/wiki/Sorting_numbers">Sorting numbers</a>.
%F A002867 a(n) = 2^n * A000246(n+1).
%F A002867 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
%F A002867 Conjecture: a(n) - 2*a(n-1) - 4*n*(n-1)*a(n-2) = 0. - _R. J. Mathar_, Nov 24 2012
%F A002867 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
%t A002867 Table[Binomial[n,Floor[n/2]](n+1)!,{n,0,20}] (* _Harvey P. Dale_, Sep 04 2018 *)
%Y A002867 Cf. A000246.
%K A002867 nonn,easy
%O A002867 0,2
%A A002867 _N. J. A. Sloane_
%E A002867 More terms from _James Sellers_, Jul 10 2000