A002011 - OEIS

%I M3598 N1458 #32 Sep 04 2018 11:34:34

%S 4,24,120,560,2520,11088,48048,205920,875160,3695120,15519504,

%T 64899744,270415600,1123264800,4653525600,19234572480,79342611480,

%U 326704870800,1343120024400,5513861152800,22606830726480,92580354403680,378737813469600

%N a(n) = 4*(2n+1)!/n!^2.

%D R. C. Mullin, E. Nemeth and P. J. Schellenberg, The enumeration of almost cubic maps, pp. 281-295 in Proceedings of the Louisiana Conference on Combinatorics, Graph Theory and Computer Science. Vol. 1, edited R. C. Mullin et al., 1970.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

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

%H T. D. Noe, <a href="/A002011/b002011.txt">Table of n, a(n) for n = 0..200</a>

%H Milan Janjić, <a href="https://www.emis.de/journals/JIS/VOL21/Janjic2/janjic103.html">Pascal Matrices and Restricted Words</a>, J. Int. Seq., Vol. 21 (2018), Article 18.5.2.

%F G.f.: 4*(1-4x)^(-3/2).

%F a(n) = 1/J(n) where J(n) = Integral_{t=0..Pi/4} (cos(t)^2 - 1/2)^(2n+1). - _Benoit Cloitre_, Oct 17 2006

%p seq(2*n*binomial(2*n,n), n=1..23); # _Zerinvary Lajos_, Dec 14 2007

%t Table[4*(2*n + 1)!/n!^2, {n, 0, 20}] (* _T. D. Noe_, Aug 30 2012 *)

%o (PARI) a(n)=if(n<0,0,4*(2*n+1)!/n!^2)

%Y a(n)=4 A002457(n).

%Y a(n) = 2 * A005430(n+1) = 4 * A002457(n).

%Y Cf. A001803.

%K nonn

%O 0,1

%A _N. J. A. Sloane_, _Simon Plouffe_

%E Simpler description from Travis Kowalski (tkowalski(AT)coloradocollege.edu), Mar 20 2003