A000506 One half of the number of permutations of [n] such that the differences have 5 runs with the same signs.

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

Offset: 6

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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).

Crossrefs

A diagonal of A008970.

Programs

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 *)

Formula

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

Extensions

More terms from Emeric Deutsch, Feb 21 2004