0,3

Number of permutations beginning with 21 and avoiding 1-23. - Ralf Stephan, Apr 25 2004

Originally defined as main diagonal of an array of binomial recurrence coefficients (see Gould).

H. W. Gould, A linear binomial recurrence and the Bell numbers and polynomials, to appear

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

S. Kitaev and T. Mansour, Simultaneous avoidance of generalized patterns.

a(n) = b(n-2), n>1, b(n) = Sum_{k = 1..n} binomial(n, k-1)*b(n-k), b(0) = 1. - Vladeta Jovovic (vladeta(AT)Eunet.yu), Apr 28 2001

E.g.f. satisfies A'(x) = exp(x)*A(x)+1 [ njas ]

With offset 0, e.g.f.: x + exp(exp(x)) * int[0..x, t*exp(-exp(t)+t) dt] (fits the recurrence up to n=215). - Ralf Stephan, Apr 25 2004

Recurrence : a(1)=1, a(2)=1, for n>2, a(n)=n-1+sum(j=2, n-1, binomial(n-1, j)*a(j)) [gives a(n+1)] - Jon Perry (perry(AT)globalnet.co.uk), Apr 26 2005

Left-hand border of triangle A046936.

Sequence in context: A066571 A087648 A086616 this_sequence A071603 A090595 A027040

Adjacent sequences: A040024 A040025 A040026 this_sequence A040028 A040029 A040030

easy,nonn,nice

H. W. Gould (gould(AT)math.wvu.edu)

Entry revised by njas, Dec 11 2006