%I A010028
%S A010028 1,1,0,1,2,0,1,5,5,1,1,8,24,20,7,1,11,60,128,115,45,1,14,113,444,835,
%T A010028 790,323,1,17,183,1099,3599,6423,6217,2621,1,20,270,2224,11060,
%U A010028 32484,56410,55160,23811,1,23,374,3950,27152
%N A010028 Triangle read by rows: T(n,k) = one-half the number of permutations of 
               length n with exactly n-k rising or falling successions, for n >= 
               1, 1 <= k <= n. T(1,0) = 1 by convention.
%C A010028 (1/2) times number of permutations of 12...n such that exactly n-k of 
               the following occur: 12, 23, ..., (n-1)n, 21, 32, ..., n(n-1).
%D A010028 F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied 
               Tables, Cambridge, 1966, p. 263.
%D A010028 J. Riordan, A recurrence for permutations without rising or falling successions. 
               Ann. Math. Statist. 36 (1965), 708-710.
%F A010028 For n>1, coefficient of t^(n-k) in S[n](t) defined in A002464, divided 
               by 2.
%e A010028 1; 1,0; 1,2,0; 1,5,5,1; 1,8,24,20,7; ...
%Y A010028 Diagonals give A001266 (and A002464), A000130, A000349, A001267, A001268.
%Y A010028 Triangle in A086856 transposed. Cf. A001100.
%Y A010028 Sequence in context: A086810 A085838 A094456 this_sequence A151860 A089627 
               A055925
%Y A010028 Adjacent sequences: A010025 A010026 A010027 this_sequence A010029 A010030 
               A010031
%K A010028 tabl,nonn
%O A010028 1,5
%A A010028 N. J. A. Sloane (njas(AT)research.att.com).