A002011 a(n) = 4*(2n+1)!/n!^2. (Formerly M3598 N1458)

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

Offset

0,1

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.

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

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 *)

Prog

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

Crossrefs

a(n)=4 A002457(n).

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

Cf. A001803.

Sequence in context: A037132 A067312 A017976 * A270462 A273444 A049315

Adjacent sequences: A002008 A002009 A002010 * A002012 A002013 A002014

Keyword

nonn

Author

N. J. A. Sloane, Simon Plouffe

Extensions

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

Status

approved