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%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
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