A129149
Permutations with exactly 7 fixed points.
Original entry on oeis.org
1, 0, 36, 240, 2970, 34848, 454740, 6362928, 95450355, 1527194240, 25962321528, 467321755680, 8879113408308, 177582268088640, 3729227629977720, 82043007859339296, 1886989180765048965, 45287740338360829056
Offset: 7
-
a:=n->sum(n!*sum((-1)^k/(k-6)!, j=0..n), k=6..n): seq(a(n)/7!, n=6..24);
restart: G(x):=exp(-x)/(1-x)*(x^7/7!): f[0]:=G(x): for n from 1 to 26 do f[n]:=diff(f[n-1],x) od: x:=0: seq(f[n],n=7..24); # Zerinvary Lajos, Apr 03 2009
-
With[{nn=40}, Drop[CoefficientList[Series[Exp[-x]/(1 - x) x^7/7!, {x, 0, nn}], x]Range[0, nn]!, 7]] (* Vincenzo Librandi, Feb 19 2014 *)
-
x='x+O('x^66); Vec( serlaplace(exp(-x)/(1-x)*(x^7/7!)) ) \\ Joerg Arndt, Feb 19 2014
A129153
Rencontres numbers: permutations with exactly 8 fixed points.
Original entry on oeis.org
1, 0, 45, 330, 4455, 56628, 795795, 11930490, 190900710, 3245287760, 58415223438, 1109889169740, 22197783520770, 466153453732680, 10255375982438730, 235873647595600476, 5660967542295146895, 141524188557377590800
Offset: 8
-
a:= n-> -sum((n-1)!*sum((-1)^k/(k-7)!, j=0..n-1), k=7..n-1)/8!: seq(a(n), n=8..30);
-
With[{nn=40}, Drop[CoefficientList[Series[Exp[-x]/(1 - x) x^8/8!, {x, 0, nn}], x]Range[0, nn]!, 8]] (* Vincenzo Librandi, Feb 19 2014 *)
-
x='x+O('x^66); Vec( serlaplace(exp(-x)/(1-x)*(x^8/8!)) ) \\ Joerg Arndt, Feb 19 2014
A129217
Permutations with exactly 9 fixed points.
Original entry on oeis.org
1, 0, 55, 440, 6435, 88088, 1326325, 21209760, 360590230, 6490575520, 123321027258, 2466420377200, 51794828215130, 1139486220235440, 26208183066232310, 628996393588267936, 15724909839708741375
Offset: 9
-
a:=n->sum(n!*sum((-1)^k/(k-8)!, j=0..n), k=8..n): seq(a(n)/9!, n=8..27);
restart: G(x):=exp(-x)/(1-x)*(x^9/9!): f[0]:=G(x): for n from 1 to 26 do f[n]:=diff(f[n-1],x) od: x:=0: seq(f[n],n=9..25); # Zerinvary Lajos, Apr 03 2009
-
With[{nn=40}, Drop[CoefficientList[Series[Exp[-x]/(1 - x) x^9/9!, {x, 0, nn}], x]Range[0, nn]!, 9]] (* Vincenzo Librandi, Feb 19 2014 *)
-
x='x+O('x^66); Vec( serlaplace(exp(-x)/(1-x)*(x^9/9!)) ) \\ Joerg Arndt, Feb 19 2014
A129238
Permutations with exactly 11 fixed points.
Original entry on oeis.org
1, 0, 78, 728, 12285, 192192, 3279640, 59001696, 1121107806, 22421988160, 470862104076, 10358965584240, 238256209789598, 5718149032454208, 142953725815812600, 3716796871203401440, 100353515522504876775
Offset: 11
-
a:=n->sum(n!*sum((-1)^k/(k-10)!, j=0..n), k=10..n): seq(a(n)/11!, n=10..27);
restart: G(x):=exp(-x)/(1-x)*(x^11/11!): f[0]:=G(x): for n from 1 to 29 do f[n]:=diff(f[n-1],x) od: x:=0: seq(f[n],n=11..27); # Zerinvary Lajos, Apr 03 2009
-
With[{nn=40}, Drop[CoefficientList[Series[Exp[-x]/(1 - x) x^11/11!, {x, 0, nn}], x]Range[0, nn]!, 11]] (* Vincenzo Librandi, Feb 19 2014 *)
-
x='x+O('x^66); Vec( serlaplace(exp(-x)/(1-x)*(x^11/11!)) ) \\ Joerg Arndt, Feb 19 2014
A129255
Permutations with exactly 12 fixed points.
Original entry on oeis.org
1, 0, 91, 910, 16380, 272272, 4919460, 93419352, 1868513010, 39238479280, 863247190806, 19854684036460, 476512419579196, 11912810484279600, 309733072600927300, 8362792960207653240, 234158202885844712475
Offset: 12
-
a:=n->sum(n!*sum((-1)^k/(k-11)!, j=0..n), k=11..n): seq(-a(n)/12!, n=11..28);
restart: G(x):=exp(-x)/(1-x)*(x^12/12!): f[0]:=G(x): for n from 1 to 29 do f[n]:=diff(f[n-1],x) od: x:=0: seq(f[n],n=12..28);# Zerinvary Lajos, Apr 03 2009
-
With[{nn=40}, Drop[CoefficientList[Series[Exp[-x]/(1 - x) x^12/12!, {x, 0, nn}], x]Range[0, nn]!, 12]] (* Vincenzo Librandi, Feb 19 2014 *)
-
x='x+O('x^66); Vec( serlaplace(exp(-x)/(1-x)*(x^12/12!)) ) \\ Joerg Arndt, Feb 19 2014