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 A263885 Number of permutations of [n] containing exactly one occurrence of the consecutive pattern 132. 3
 1, 8, 54, 368, 2649, 20544, 172596, 1569408, 15398829, 162412416, 1834081890, 22093090560, 282889238253, 3837991053312, 55010010678120, 830731742908416, 13185328329110745, 219457733809563648, 3822426663111579150, 69538569862816419840, 1318999546575572747265 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,2 LINKS Alois P. Heinz, Table of n, a(n) for n = 3..200 Eric Weisstein's World of Mathematics, Inverse Erf FORMULA a(n) = A197365(n,1). a(n) ~ c * d^n * n! * n, where d = 1/A240885 = 1/(sqrt(2) * InverseErf(sqrt(2/Pi))) = 0.78397693120354749... and c = 0.679554202696108785... . - Vaclav Kotesovec, Oct 29 2015 EXAMPLE a(3) = 1: 132. a(4) = 8: 1243, 1324, 1423, 1432, 2143, 2431, 3142, 4132. a(5) = 54: 12354, 12435, 12534, ..., 52431, 53142, 54132. a(6) = 368: 123465, 123546, 123645, ..., 652431, 653142, 654132. a(7) = 2649: 1234576, 1234657, 1234756, ..., 7652431, 7653142, 7654132. MAPLE b:= proc(u, o, t, c) option remember; `if`(u+o=0, c, add(       b(u-j, o+j-1, 0, c+`if`(j<=t, 1, 0)), j=`if`(c=1, t, 0)       +1..u) +add(b(u+j-1, o-j, j-1, c), j=1..o))     end: a:= n-> b(n, 0\$3): seq(a(n), n=3..30); MATHEMATICA Drop[Coefficient[CoefficientList[Series[1/(1 - (Sqrt[Pi/2]*Erfi[(Sqrt[u-1]*x) / Sqrt[2]])/Sqrt[u-1]), {x, 0, 25}], x] * Range[0, 25]!, u], 3] (* Vaclav Kotesovec, Oct 29 2015 *) CROSSREFS Column k=1 of A197365. Sequence in context: A289796 A287814 A201640 * A002775 A079754 A298985 Adjacent sequences:  A263882 A263883 A263884 * A263886 A263887 A263888 KEYWORD nonn AUTHOR Alois P. Heinz, Oct 28 2015 STATUS approved

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Last modified July 28 11:50 EDT 2021. Contains 346328 sequences. (Running on oeis4.)