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A221957 Number of n X n rook placements avoiding the pattern 012. 1
1, 2, 7, 31, 159, 921, 5988, 43632, 355491, 3223729, 32329668, 355979064, 4273100846, 55555511298, 777797216472, 11667035805840, 186672873433635, 3173440015174905, 57121924810715940, 1085316589076234760, 21706331850447959610, 455832969128536089030 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Dan Daly and Lara Pudwell, Pattern avoidance in rook monoids, Special Session on Patterns in Permutations and Words, Joint Mathematics Meetings, 2013.

FORMULA

From Vaclav Kotesovec, Feb 07 2013: (Start)

E.g.f.: 1/2*(exp(2*x)*BesselI(0,2*x)+1)/(1-x).

Recurrence: n*a(n) = (n^2+4*n-2)*a(n-1)-2*(n-1)*(2*n-1)*a(n-2).

a(n) ~ c * n!, where c = (exp(2)*BesselI(0,2)+1)/2 = 8.921991840629494...

(End)

c = 1 + Sum_{k>=0} binomial(2*k+1,k) / (k+1)!. - Vaclav Kotesovec, Jul 19 2021

MATHEMATICA

CoefficientList[Series[1/2*(Exp[2*x]*BesselI[0, 2*x]+1)/(1-x), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Feb 07 2013 *)

PROG

(PARI) a(n) = {sum(k=0, n, if (k==n, n!, sum(j=1, k+1, binomial(n-j, n-k-1)*binomial(n, k)*binomial(k, j-1)*(j-1)!))); } \\ Michel Marcus, Feb 07 2013

CROSSREFS

Sequence in context: A030882 A273957 A221958 * A030966 A009132 A125275

Adjacent sequences:  A221954 A221955 A221956 * A221958 A221959 A221960

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Feb 04 2013

EXTENSIONS

More terms from Michel Marcus, Feb 07 2013

STATUS

approved

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Last modified October 20 13:38 EDT 2021. Contains 348108 sequences. (Running on oeis4.)