A230233 Number of permutations of [n] avoiding adjacent step pattern {up}^10.

1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916799, 479001577, 6227020358, 87178283010, 1307674215120, 20922786961440, 355687370176320, 6402372516146880, 121645075013280000, 2432901444395385600, 51090929159028595200, 1124000415686590747031

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..450

Formula

E.g.f.: 1 / Sum_{n>=0} (11*n+1-x)*x^(11*n)/(11*n+1)!.

a(n)/n! ~ 1.000000227556759905306252970186381144189779110025896440589711080508... * (1/r)^n, where r = 1.000000022964438439732421879840792836238519233492197325926442472620564... is the root of the equation Sum_{n>=0} (r^(11*n)/(11*n)! - r^(11*n+1)/(11*n+1)!) = 0. - Vaclav Kotesovec, Jan 17 2015

E.g.f.: -11/(2*((-cos(x*cos(Pi/22)))* cosh(x*sin(Pi/22)) - cos(x*cos(3*Pi/22))* cosh(x*sin(3*Pi/22)) - cos(x*cos(5*Pi/22))* cosh(x*sin(5*Pi/22)) - cos(x*cos(Pi/22))* cosh(x*sin(Pi/22))*sin(Pi/22) + cos(x*cos(3*Pi/22))* cosh(x*sin(3*Pi/22))* sin(3*Pi/22) - cos(x*cos(5*Pi/22))* cosh(x*sin(5*Pi/22))* sin(5*Pi/22) + cos(Pi/22)* cosh(x*sin(Pi/22))* sin(x*cos(Pi/22)) + cos(3*Pi/22)*cosh( x*sin(3*Pi/22))* sin(x*cos(3*Pi/22)) + cos(5*Pi/22)*cosh( x*sin(5*Pi/22))* sin(x*cos(5*Pi/22)) - cosh(x*cos(Pi/11))* ((1 + cos(Pi/11))* cos(x*sin(Pi/11)) - sin(Pi/11)*sin(x*sin(Pi/11))) + cosh(x*cos(2*Pi/11))* ((-1 + cos(2*Pi/11))* cos(x*sin(2*Pi/11)) + sin(2*Pi/11)* sin(x*sin(2*Pi/11))) + cos(x*sin(Pi/11))* sinh(x*cos(Pi/11)) + cos(Pi/11)*cos(x*sin(Pi/11))* sinh(x*cos(Pi/11)) - sin(Pi/11)*sin(x*sin(Pi/11))* sinh(x*cos(Pi/11)) - cos(x*sin(2*Pi/11))* sinh(x*cos(2*Pi/11)) + cos(2*Pi/11)* cos(x*sin(2*Pi/11))* sinh(x*cos(2*Pi/11)) + sin(2*Pi/11)* sin(x*sin(2*Pi/11))* sinh(x*cos(2*Pi/11)) + cos(x*cos(Pi/22))* sinh(x*sin(Pi/22)) + cos(x*cos(Pi/22))*sin(Pi/22)* sinh(x*sin(Pi/22)) - cos(Pi/22)*sin(x*cos(Pi/22))* sinh(x*sin(Pi/22)) - cos(x*cos(3*Pi/22))* sinh(x*sin(3*Pi/22)) + cos(x*cos(3*Pi/22))* sin(3*Pi/22)* sinh(x*sin(3*Pi/22)) + cos(3*Pi/22)* sin(x*cos(3*Pi/22))* sinh(x*sin(3*Pi/22)) + cos(x*cos(5*Pi/22))* sinh(x*sin(5*Pi/22)) + cos(x*cos(5*Pi/22))* sin(5*Pi/22)* sinh(x*sin(5*Pi/22)) - cos(5*Pi/22)* sin(x*cos(5*Pi/22))* sinh(x*sin(5*Pi/22)))). - Vaclav Kotesovec, Jan 31 2015

Maple

b:= proc(u, o, t) option remember; `if`(u+o=0, 1,
      `if`(t<9, add(b(u+j-1, o-j, t+1), j=1..o), 0)+
      add(b(u-j, o+j-1, 0), j=1..u))
    end:
a:= n-> b(n, 0, 0):
seq(a(n), n=0..30);

Mathematica

nn=20; r=10; a=Apply[Plus, Table[Normal[Series[y x^(r+1)/(1-Sum[y x^i, {i, 1, r}]), {x, 0, nn}]][[n]]/(n+r)!, {n, 1, nn-r}]]/.y->-1; Range[0, nn]! CoefficientList[Series[1/(1-x-a), {x, 0, nn}], x] (* Geoffrey Critzer, Feb 25 2014 *)
CoefficientList[Series[1/(HypergeometricPFQ[{}, {1/11, 2/11, 3/11, 4/11, 5/11, 6/11, 7/11, 8/11, 9/11, 10/11}, x^11/285311670611] - x*HypergeometricPFQ[{}, {2/11, 3/11, 4/11, 5/11, 6/11, 7/11, 8/11, 9/11, 10/11, 12/11}, x^11/285311670611]), {x, 0, 25}], x] * Range[0, 25]! (* Vaclav Kotesovec, Jan 17 2015 *)

Crossrefs

Cf. A049774, A117158, A177523, A177533, A177553, A230051, A230231, A230232.

Column k=1023 of A242784.

Sequence in context: A360463 A193937 A072167 * A154659 A254523 A289282

Adjacent sequences: A230230 A230231 A230232 * A230234 A230235 A230236

Keyword

nonn

Author

Alois P. Heinz, Oct 12 2013

Status

approved