%I A000130 M1528 N0598
%S A000130 0,0,1,2,5,20,115,790,6217,55160,545135,5938490,70686805,912660508,12702694075,
%T A000130 189579135710,3019908731105,51139445487680,917345570926087,17376071107513090,
%U A000130 346563420097249645,7259714390232227300,159352909727731210835,3657569576966074846118
%N A000130 One-half the number of permutations of length n with exactly 1 rising 
               or falling successions.
%C A000130 (1/2) times number of permutations of 12...n such that exactly one of 
               the following occurs: 12, 23, ..., (n-1)n, 21, 32, ..., n(n-1).
%C A000130 Partial sums seem to be in A000239. - Ralf Stephan (ralf(AT)ark.in-berlin.de), 
               Aug 28 2003
%D A000130 F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied 
               Tables, Cambridge, 1966, p. 263.
%D A000130 J. Riordan, A recurrence for permutations without rising or falling successions. 
               Ann. Math. Statist. 36 (1965), 708-710.
%D A000130 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000130 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%F A000130 Coefficient of t^1 in S[n](t) defined in A002464, divided by 2.
%Y A000130 Cf. A002464, A086853. Equals A086852/2. A diagonal of A010028.
%Y A000130 Sequence in context: A129949 A127065 A052850 this_sequence A009599 A112833 
               A144503
%Y A000130 Adjacent sequences: A000127 A000128 A000129 this_sequence A000131 A000132 
               A000133
%K A000130 nonn
%O A000130 0,4
%A A000130 N. J. A. Sloane (njas(AT)research.att.com).