

A000239


Onehalf of number of permutations of [n] with exactly one run of adjacent symbols differing by 1.
(Formerly M2758 N1109)


3



1, 1, 3, 8, 28, 143, 933, 7150, 62310, 607445, 6545935, 77232740, 989893248, 13692587323, 203271723033, 3223180454138, 54362625941818, 971708196867905, 18347779304380995, 364911199401630640, 7624625589633857940, 166977535317365068775, 3824547112283439914893, 91440772473772839055238
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OFFSET

1,3


COMMENTS

First differences seem to be in A000130.  Ralf Stephan, Aug 28 2003


REFERENCES

F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 264, Table 7.6.2.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


LINKS

JeanFrançois Alcover, Table of n, a(n) for n = 1..40


EXAMPLE

The permutation 3 2 1 4 5 7 6 has three such runs: 321, 45 and 76.
For n<=3 all permutations have one such run. For n=4, 16 have one run, two have no such runs (2413 and 3142), and 6 have two runs (1243, 2134, 2143, 3412, 3421), so a(4) = 16/2 = 8.


MATHEMATICA

S[n_] := S[n] = If[n<4, {1, 1, 2*t, 4*t + 2*t^2}[[n+1]], (n+1t)* S[n1]  (1t)*(n2+3*t)*S[n2]  (1t)^2*(n5+t)*S[n3] + (1t)^3*(n3)*S[n4]]; A000239 = Join[{1}, Table[Coefficient[S[n], t, 1]/2, {n, 1, 20}] // Accumulate // Rest] (* JeanFrançois Alcover, Feb 06 2016, from successive accumulation of A000130 *)


CROSSREFS

This is a diagonal of the irregular triangle in A010030.
Sequence in context: A009437 A000776 A327030 * A268302 A195687 A060707
Adjacent sequences: A000236 A000237 A000238 * A000240 A000241 A000242


KEYWORD

nonn


AUTHOR

N. J. A. Sloane


EXTENSIONS

Entry revised by N. J. A. Sloane, Apr 14 2014
More terms from JeanFrançois Alcover, Feb 06 2016


STATUS

approved



