A324137 - OEIS

%I #18 May 30 2026 16:40:48

%S 1,1,2,6,24,120,720,5020,39790,352470,3445032,36775404,425282892,

%T 5292245764,70471602994,999394962306,15032677450752,238984379214960,

%U 4002966472631160,70448661940661068,1299478739106621670,25067231918730741438,504674373639695198712,10584965637367018566180

%N Number of permutations of [n] that avoid the shuffle pattern s-k-t, where s = 123 and t = 123.

%H Sergey Kitaev, <a href="https://doi.org/10.1016/j.disc.2004.03.017">Partially Ordered Generalized Patterns</a>, Discrete Math. 298 (2005), no. 1-3, 212-229.

%F Let b(n) = A049774(n) = number of permutations avoiding a consecutive 123 pattern. Then a(n) = Sum_{i = 0..n-1} binomial(n-1,i) (2*b(i)*a(n-1-i) - b(i)*b(n-1-i)) for n >= 1 with a(0) = b(0) = 1. [See the recurrence for C_n on p. 220 of Kitaev (2005).] - _Petros Hadjicostas_, Oct 30 2019

%Y Cf. A000142, A049774.

%K nonn

%O 0,3

%A _N. J. A. Sloane_, Feb 16 2019

%E More terms from _Petros Hadjicostas_, Oct 31 2019