%I M5322 N2313
%S 61,841,7311,51663,325446,1910706,10715506,58258210,309958755,
%T 1623847695,8412276585,43220104041,220683627988,1121561317408,
%U 5679711010548,28683869195556,144552802373145,727271783033445
%N One half of the number of permutations of [n] such that the differences have 5 runs with the same signs.
%D L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 260, #13
%D F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 260.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%F Lim_{n>infinity} 16*a(n)/5^n = 1.  _Philippe Deléham_, Feb 22 2004
%t 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 *)
%Y A diagonal of A008970.
%K nonn,easy
%O 6,1
%A _N. J. A. Sloane_
%E More terms from _Emeric Deutsch_, Feb 21 2004
