A238917 Number of self-inverse permutations p on [n] where the maximal displacement of an element equals 6.

0, 0, 0, 0, 0, 0, 0, 26, 142, 544, 1826, 5651, 16859, 49739, 147605, 437656, 1292876, 3795660, 11066720, 32052260, 92323188, 264835528, 757301423, 2159899295, 6146377790, 17454698660, 49473876635, 139980358007, 395414558802, 1115322187106, 3141769710776

Offset: 0

Author

Joerg Arndt and Alois P. Heinz, Mar 07 2014

Keywords

• nonn

Examples

			a(7) = 26: 7234561, 7234651, 7235461, 7236541, 7243561, 7243651, 7254361, 7256341, 7264531, 7265431, 7324561, 7324651, 7325461, 7326541, 7432561, 7432651, 7452361, 7462531, 7534261, 7536241, 7543261, 7564231, 7634521, 7635421, 7643521, 7654321.
a(8) = 142: 18345672, 18345762, 18346572, ..., 78563412, 78645312, 78654312.
		

Links

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

Crossrefs

Column k=6 of A238889.

Programs

Maple

gf:= -(x^79 +x^78 +2*x^77 -2*x^76 -4*x^75 -2*x^74 -2*x^73 -4*x^72 -2*x^71 -16*x^70 -10*x^69 -8*x^68 +2*x^67 +6*x^66 -2*x^65 +34*x^64 +82*x^63 +248*x^62 +114*x^61 +360*x^60 -176*x^59 +16*x^58 -613*x^57 -241*x^56 +286*x^55 +200*x^54 +812*x^53 -304*x^52 -2614*x^51 -6192*x^50 -1748*x^49 -2174*x^48 +3692*x^47 +4660*x^46 +8104*x^45 -2394*x^44 -6262*x^43 -4118*x^42 -8486*x^41 -2952*x^40 +12820*x^39 +22770*x^38 +6232*x^37
+18124*x^36 +16806*x^35 -8932*x^34 -17752*x^33 -4328*x^32 -688*x^31 -11856*x^30 +1494*x^29 +7926*x^28 -1271*x^27 -15619*x^26 -17708*x^25 -10526*x^24 -15064*x^23 -5448*x^22 +4982*x^21 +7232*x^20 +6266*x^19 +4794*x^18 +4536*x^17 -1642*x^16 -4844*x^15 -1982*x^14 +1702*x^13 +3180*x^12 +2406*x^11 +2236*x^10 +1808*x^9 +844*x^8 -232*x^7 -712*x^6 -427*x^5 -23*x^4 +132*x^3 +130*x^2 +90*x +26)*x^7 /
(-x^96 -2*x^95 -5*x^94 -2*x^93 +x^92 +4*x^91 +x^90 -6*x^89 +7*x^88 +22*x^87 +29*x^86 +33*x^85 +91*x^84 +80*x^83 +145*x^82 -10*x^81 -131*x^80 -408*x^79 -373*x^78 -190*x^77 +37*x^76 -116*x^75 -944*x^74 -1228*x^73 -3013*x^72 -912*x^71 -41*x^70 +5598*x^69 +6515*x^68 +5412*x^67 +313*x^66 -6440*x^65 -6653*x^64 +8601*x^63 +33249*x^62
+25690*x^61 +16607*x^60 -20970*x^59 -36849*x^58 -58454*x^57 -2951*x^56 +45112*x^55 +57779*x^54 +50354*x^53 -7307*x^52 -120264*x^51 -203634*x^50 -94356*x^49 -44544*x^48 -80*x^47 +29346*x^46 +69552*x^45 -7775*x^44 -30206*x^43 +20425*x^42 +98686*x^41 +199971*x^40 +199712*x^39 +213579*x^38 +115272*x^37 +13389*x^36 -79542*x^35 -80901*x^34
-67351*x^33 -61223*x^32 +3440*x^31 +91*x^30 -40746*x^29 -103061*x^28 -115084*x^27 -94543*x^26 -59162*x^25 -2547*x^24 +37784*x^23 +58688*x^22 +53020*x^21 +43683*x^20 +26240*x^19 +6089*x^18 -3934*x^17 -5143*x^16 -3776*x^15 -3661*x^14 -1868*x^13 -975*x^12 -827*x^11 -517*x^10 -330*x^9 -23*x^8 +64*x^7 -3*x^6 -10*x^5 -5*x^4 -4*x^3 +5*x^2 +2*x -1):
a:= n-> coeff(series(gf, x, n+1), x, n):
seq(a(n), n=0..40);

Formula

G.f.: see Maple program.