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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)
3

%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[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 *)

%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

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Last modified February 17 10:59 EST 2019. Contains 320219 sequences. (Running on oeis4.)