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A000506

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

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[n-1, k] + 2*p[n-1, k-1] + (n-k)*p[n-1, k-2]; p[n_, k_] = 0; t[n_, k_] := p[n, k]/2; a[n_] := t[n, 5]; Table[a[n], {n, 6, 23}] (* Jean-François Alcover, Feb 09 2016 *)

CROSSREFS

A diagonal of A008970.

Sequence in context: A232858 A373724 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