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

Author

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

Keywords

• nonn
• nice
• easy
• eigen

Comments

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

Links

• 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.

Crossrefs

Cf. A032347, A046934.

Programs

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 *)

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

Extensions

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