A032346 Essentially shifts 1 place right under inverse binomial transform.

1, 1, 2, 6, 21, 82, 354, 1671, 8536, 46814, 273907, 1700828, 11158746, 77057021, 558234902, 4230337018, 33448622893, 275322101318, 2354401779494, 20878592918183, 191682453823420, 1819147694792802, 17822073621801123

Offset

0,3

Comments

With leading 0 and offset 1, number of permutations beginning with 21 and avoiding 3-12. - Ralf Stephan, Apr 25 2004

Links

Table of n, a(n) for n=0..22.

N. J. A. Sloane, Transforms

Sergey Kitaev, Generalized pattern avoidance with additional restrictions, Sem. Lothar. Combinat. 48 (2003), Article B48e.

Sergey Kitaev, Partially Ordered Generalized Patterns, Discrete Math. 298(1-3) (2005), 212-229.

Sergey Kitaev and Toufik Mansour, Simultaneous avoidance of generalized patterns, arXiv:math/0205182 [math.CO], 2002.

Formula

With offset 1, e.g.f.: x + exp(exp(x)) * int[0..x, exp(-exp(t))*sum(n>=1, t^n/n!) dt]. - Ralf Stephan, Apr 25 2004

Mathematica

max = 23; f[x_] = x + Exp[Exp[x]]*Integrate[Exp[-Exp[t]]*Sum[t^n/n!, {n, 1, max}], {t, 0, x}]; Rest[ CoefficientList[ Series[f[x], {x, 0, max}], x]*Range[0, max]!] (* Jean-François Alcover, Aug 07 2012, after Ralf Stephan *)

Crossrefs

Cf. A032347, A046934.

Sequence in context: A279567 A281784 A032347 * A329055 A148495 A150221

Adjacent sequences: A032343 A032344 A032345 * A032347 A032348 A032349

Keyword

nonn,nice,easy,eigen

Author

Joe K. Crump (joecr(AT)carolina.rr.com)

Extensions

Last digit of a(22) corrected by Jean-François Alcover, Aug 07 2012

Status

approved