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A270049 Number of 123 avoiding set partitions of [n]. 1
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 (list; graph; refs; listen; history; text; internal format)
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 A148670 A148671

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

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Last modified May 13 05:02 EDT 2021. Contains 343836 sequences. (Running on oeis4.)