cp's OEIS Frontend

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

%I A230233 #20 Aug 16 2018 16:03:21
%S A230233 1,1,2,6,24,120,720,5040,40320,362880,3628800,39916799,479001577,
%T A230233 6227020358,87178283010,1307674215120,20922786961440,355687370176320,
%U A230233 6402372516146880,121645075013280000,2432901444395385600,51090929159028595200,1124000415686590747031
%N A230233 Number of permutations of [n] avoiding adjacent step pattern {up}^10.
%H A230233 Alois P. Heinz, <a href="/A230233/b230233.txt">Table of n, a(n) for n = 0..450</a>
%F A230233 E.g.f.: 1 / Sum_{n>=0} (11*n+1-x)*x^(11*n)/(11*n+1)!.
%F A230233 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
%F A230233 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
%p A230233 b:= proc(u, o, t) option remember; `if`(u+o=0, 1,
%p A230233       `if`(t<9, add(b(u+j-1, o-j, t+1), j=1..o), 0)+
%p A230233       add(b(u-j, o+j-1, 0), j=1..u))
%p A230233     end:
%p A230233 a:= n-> b(n, 0, 0):
%p A230233 seq(a(n), n=0..30);
%t A230233 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 *)
%t A230233 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 *)
%Y A230233 Cf. A049774, A117158, A177523, A177533, A177553, A230051, A230231, A230232.
%Y A230233 Column k=1023 of A242784.
%K A230233 nonn
%O A230233 0,3
%A A230233 _Alois P. Heinz_, Oct 12 2013