A010030 - OEIS

A010030

Irregular triangle read by rows: T(n,k) (n >= 1, 0 <= k <= [n/2]) = number of permutations of 1..n with [n/2]-k runs of consecutive pairs up and down (divided by 2).

%I #11 Apr 14 2014 12:53:21

%S 1,1,0,3,0,3,8,1,25,28,7,17,155,143,45,259,1005,933,323,131,2770,7488,

%T 7150,2621,3177,27978,64164,62310,23811,1281,51433,294602,619986,

%U 607445,239653

%N Irregular triangle read by rows: T(n,k) (n >= 1, 0 <= k <= [n/2]) = number of permutations of 1..n with [n/2]-k runs of consecutive pairs up and down (divided by 2).

%D F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 264.

%F G.f. for number of permutations of 1..n by number of runs of consecutive pairs up and down is Sum(n!*(((1-y)*(2*x^2-x^3)-x)/((1-y)*x^2-1))^n,n = 0 .. infinity), cf. A010029. - _Vladeta Jovovic_, Nov 23 2007

%e Triangle begins:

%e 1,

%e 1, 0,

%e 3, 0,

%e 3, 8, 1,

%e 25, 28, 7,

%e 17, 155, 143, 45,

%e 259, 1005, 933, 323,

%e 131, 2770, 7488, 7150, 2621,

%e 3177, 27978, 64164, 62310, 23811,

%e 1281, 51433, 294602, 619986, 607445, 239653,

%e ...

%Y Cf. A002464, A001266, A000239, A000544, A001282.

%K tabf,nonn

%O 1,4

%A _N. J. A. Sloane_.

%E More terms from _Vladeta Jovovic_, Nov 23 2007

%E Entry revised by _N. J. A. Sloane_, Apr 14 2014