A099745 Number of permutations of [n] with exactly 2 valleys which avoid the permutation 1324.

0, 0, 0, 0, 12, 168, 1409, 9187, 51362, 258674, 1207855, 5326205, 22459080, 91368900, 360977373, 1391835607, 5257593566, 19515948358, 71358739003, 257521313441, 918732810340, 3244576312440, 11355547678665, 39423281302875, 135876498446042, 465248862099418

Offset

1,5

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (20,-174,860,-2641,5160,-6264,4320,-1296).

Formula

G.f.: x^5*(12-72*x+137*x^2-81*x^3) / ((1-3*x)^4*(1-2*x)^4).

a(n) = (162*(-239*2^n+80*3^(1+n)) - (9909*2^n+6128*3^n)*n - 24*(27*2^n-2*3^n)*n^2 + (27*2^n+32*3^n)*n^3) / 2592. - Colin Barker, Feb 14 2017

Prog

(PARI) concat(vector(4), Vec(x^5*(12-72*x+137*x^2-81*x^3) / ((1-3*x)^4*(1-2*x)^4) + O(x^30))) \\ Colin Barker, Feb 14 2017

Crossrefs

Cf. A000079.

Sequence in context: A190063 A160566 A324414 * A360352 A268899 A366710

Adjacent sequences: A099742 A099743 A099744 * A099746 A099747 A099748

Keyword

nonn,easy

Author

Mike Zabrocki, Nov 09 2004

Status

approved