A238916 Number of self-inverse permutations p on [n] where the maximal displacement of an element equals 5.

0, 0, 0, 0, 0, 0, 10, 48, 170, 515, 1471, 4119, 11605, 32568, 90756, 250432, 684816, 1858440, 5016359, 13484339, 36124302, 96487740, 257021991, 682958487, 1810749368, 4791502490, 12657090174, 33383355375, 87928909275, 231312358250, 607831534982, 1595624166626

Offset: 0

Author

Joerg Arndt and Alois P. Heinz, Mar 07 2014

Keywords

• nonn

Examples

			a(6) = 10: 623451, 623541, 624351, 625431, 632451, 632541, 643251, 645231, 653421, 654321.
a(7) = 48: 1734562, 1734652, 1735462, ..., 6735412, 6743512, 6754312.
a(8) = 170: 12845673, 12845763, 12846573, ..., 67583124, 67845123, 67854123.
		

Links

• Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 0..1000

Crossrefs

Column k=5 of A238889.

Programs

Maple

gf:= (x^34 +x^33 +x^32 -x^30 +7*x^29 +4*x^28 +5*x^27 +3*x^26 -7*x^25 +2*x^24 +2*x^22 -4*x^21 -14*x^20 -38*x^19 -8*x^18 -14*x^17 -52*x^16 +12*x^15 +26*x^14 -56*x^13 -53*x^12 +79*x^11 +79*x^10 +42*x^9 +55*x^8 +49*x^7 -26*x^6 -65*x^5 -35*x^4 +13*x^3 +34*x^2 +28*x +10)*x^6 / ((x^16 +x^15 +2*x^14 +x^13 +x^12 +2*x^11 +x^10 +3*x^9 -4*x^8 -5*x^7 -9*x^6 -6*x^5 -x^4 -x^3 -2*x^2 -x +1) *(x^32 +x^31 +x^30 -x^29 -x^28 +7*x^27 +5*x^26 +x^25 -5*x^24 -3*x^23 -x^22 -8*x^21 -16*x^20 +8*x^18 -40*x^17 -36*x^16 +20*x^14 +12*x^13 +64*x^12 +52*x^11 +19*x^10 -5*x^9 -13*x^8 -27*x^7 -19*x^6 +x^5 -x^4 -x^3 -3*x^2 -x +1)):
a:= n-> coeff(series(gf, x, n+1), x, n):
seq(a(n), n=0..40);

Mathematica

CoefficientList[Series[(x^34 + x^33 + x^32 - x^30 + 7 x^29 + 4 x^28 + 5 x^27 + 3 x^26 - 7 x^25 + 2 x^24 + 2 x^22 - 4 x^21 - 14 x^20 - 38 x^19 - 8 x^18 - 14 x^17 - 52 x^16 + 12 x^15 + 26 x^14 - 56 x^13 - 53 x^12 + 79 x^11 + 79 x^10 + 42 x^9 + 55 x^8 + 49 x^7 - 26 x^6 - 65 x^5 - 35 x^4 + 13 x^3 + 34 x^2 + 28 x + 10) x^6/((x^16 + x^15 + 2 x^14 + x^13 + x^12 + 2 x^11 + x^10 + 3 x^9 - 4 x^8 - 5 x^7 - 9 x^6 - 6 x^5 - x^4 - x^3 - 2 x^2 - x + 1) (x^32 + x^31 + x^30 - x^29 - x^28 + 7 x^27 + 5 x^26 + x^25 - 5 x^24 - 3 x^23 - x^22 - 8 x^21 - 16 x^20 + 8 x^18 - 40 x^17 - 36 x^16 + 20 x^14 + 12 x^13 + 64 x^12 + 52 x^11 + 19 x^10 - 5 x^9 - 13 x^8 - 27 x^7 - 19 x^6 + x^5 - x^4 - x^3 - 3 x^2 - x + 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Mar 09 2014 *)

Formula

G.f.: see Maple program.