

A000506


One half of the number of permutations of [n] such that the differences have 5 runs with the same signs.
(Formerly M5322 N2313)


3



61, 841, 7311, 51663, 325446, 1910706, 10715506, 58258210, 309958755, 1623847695, 8412276585, 43220104041, 220683627988, 1121561317408, 5679711010548, 28683869195556, 144552802373145, 727271783033445
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OFFSET

6,1


REFERENCES

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 260, #13
F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 260.
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

Table of n, a(n) for n=6..23.


FORMULA

Limit_{n>infinity} 16*a(n)/5^n = 1.  Philippe Deléham, Feb 22 2004


MATHEMATICA

p[n_ /; n >= 2, 1] = 2; p[n_ /; n >= 2, k_] /; 1 <= k <= n := p[n, k] = k*p[n1, k] + 2*p[n1, k1] + (nk)*p[n1, k2]; p[n_, k_] = 0; t[n_, k_] := p[n, k]/2; a[n_] := t[n, 5]; Table[a[n], {n, 6, 23}] (* JeanFrançois Alcover, Feb 09 2016 *)


CROSSREFS

A diagonal of A008970.
Sequence in context: A251426 A232858 A093473 * A008358 A317283 A264306
Adjacent sequences: A000503 A000504 A000505 * A000507 A000508 A000509


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane


EXTENSIONS

More terms from Emeric Deutsch, Feb 21 2004


STATUS

approved



