%I A001268 M4805 N2053
%S A001268 0,0,0,0,0,1,11,113,1099,11060,118484,1366134,16970322,226574211,3240161105,
%T A001268 49453685911,802790789101,13815657556958,251309386257874,4818622686395380,
%U A001268 97145520138758844,2054507019515346789,45484006970415223287,1052036480881734378541
%N A001268 One-half the number of permutations of length n with exactly 4 rising 
               or falling successions.
%C A001268 (1/2) times number of permutations of 12...n such that exactly 4 of the 
               following occur: 12, 23, ..., (n-1)n, 21, 32, ..., n(n-1).
%D A001268 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A001268 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A001268 F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied 
               Tables, Cambridge, 1966, p. 263.
%D A001268 J. Riordan, A recurrence for permutations without rising or falling successions. 
               Ann. Math. Statist. 36 (1965), 708-710.
%F A001268 Coefficient of t^4 in S[n](t) defined in A002464, divided by 2.
%Y A001268 Cf. A002464, A000130, A086852. Equals A086855/2. A diagonal of A010028.
%Y A001268 Sequence in context: A166572 A111463 A142483 this_sequence A065538 A104096 
               A087391
%Y A001268 Adjacent sequences: A001265 A001266 A001267 this_sequence A001269 A001270 
               A001271
%K A001268 nonn
%O A001268 0,7
%A A001268 N. J. A. Sloane (njas(AT)research.att.com).