A002011 a(n) = 4*(2n+1)!/n!^2.

4, 24, 120, 560, 2520, 11088, 48048, 205920, 875160, 3695120, 15519504, 64899744, 270415600, 1123264800, 4653525600, 19234572480, 79342611480, 326704870800, 1343120024400, 5513861152800, 22606830726480, 92580354403680, 378737813469600

Offset: 0

Author

N. J. A. Sloane, Simon Plouffe

Keywords

• nonn

References

• 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.
• 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..200
• Milan Janjić, Pascal Matrices and Restricted Words, J. Int. Seq., Vol. 21 (2018), Article 18.5.2.

Crossrefs

a(n)=4 A002457(n).

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

Cf. A001803.

Programs

Maple

seq(2*n*binomial(2*n,n), n=1..23); # Zerinvary Lajos, Dec 14 2007

Mathematica

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

PARI

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

Formula

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

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

Extensions

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