A270049 Number of 123 avoiding set partitions of [n].

1, 1, 3, 7, 21, 61, 199, 659, 2345, 8569, 32971, 130527, 538045, 2279733, 9987727, 44897131, 207693905, 983926001, 4780294291, 23740460215, 120595843941, 625175300653, 3308054119767, 17837452131139, 98006292402553, 548026191197801, 3118110841312091

Offset

0,3

Links

Charles R Greathouse IV, Table of n, a(n) for n = 0..799

B. E. Sagan, Pattern avoidance in set partitions, arxiv:math/0604292 [math.CO], 2006, Theorems 2.5 and 3.4.

Formula

a(n) = Sum_{i=0..n/2} binomial(n,2*i)*(2*i)!!.

a(n) - 2*a(n-1) - (n-1)*a(n-2) + (n-2)*a(n-3) = 0.

Maple

A270049 := proc(n)
    add( binomial(n, 2*i)*doublefactorial(2*i), i=0..n/2) ;
end proc:

Mathematica

Table[Sum[Binomial[n, 2 i] (2 i)!!, {i, 0, n}], {n, 0, 26}] (* Michael De Vlieger, Mar 09 2016 *)

Prog

(PARI) a(n)=my(b=1, df=1, t); sum(i=1, n\2, t+=2; b*=(n-t+2)*(n-t+1)/(t*(t-1)); df*=t; b*df)+1 \\ Charles R Greathouse IV, Mar 10 2016

Crossrefs

Cf. A220913.

Sequence in context: A182399 A025235 A129366 * A166358 A369528 A148670

Adjacent sequences: A270046 A270047 A270048 * A270050 A270051 A270052

Keyword

nonn,easy

Author

R. J. Mathar, Mar 09 2016

Extensions

False conjecture deleted by Colin Barker, Oct 13 2016

Status

approved