A124007
Number of permutations of n distinct letters (ABCD...) each of which appears thrice with n-3 fixed points.
Original entry on oeis.org
0, 0, 54, 216, 540, 1080, 1890, 3024, 4536, 6480, 8910, 11880, 15444, 19656, 24570
Offset: 0
Maple produces the following triangle - the entries in quotes give the sequence:
1
"0", 0, 0, 1
1, 0, 9, "0", 9, 0, 1
56, 216, 378, 435, 324, 189, "54", 27, 0, 1
13833, 49464, 84510, 90944, 69039, 38448, 16476, 5184, 1431, "216", 54, 0, 1
6699824, 23123880, 38358540, 40563765, 30573900, 17399178, 7723640, 2729295, 776520, 180100, 33372, 5355, "540", 90, 0, 1
etc...
-
p := (x, k)->k!^2*sum(x^j/((k-j)!^2*j!), j=0..k); R := (x, n, k)->p(x, k)^n; f := (t, n, k)->sum(coeff(R(x, n, k), x, j)*(t-1)^j*(n*k-j)!, j=0..n*k); for n from 0 to 6 do seq(coeff(f(t, n, 3), t, m)/3!^n, m=0..3*n); od;
A124008
Number of permutations of n distinct letters (ABCD...) each of which appears thrice with n-4 fixed points.
Original entry on oeis.org
9, 189, 1431, 5355, 14310, 31374, 60354, 105786, 172935, 267795, 397089, 568269
Offset: 0
1
0, 0, 0, 1
1, 0, "9", 0, 9, 0, 1
56, 216, 378, 435, 324, "189", 54", 27, 0, 1
13833, 49464, 84510, 90944, 69039, 38448, 16476, 5184, "1431", 216, 54, 0, 1
6699824, 23123880, 38358540, 40563765, 30573900, 17399178, 7723640, 2729295, 776520, 180100, 33372, "5355", 540, 90, 0, 1
etc...
-
p := (x, k)->k!^2*sum(x^j/((k-j)!^2*j!), j=0..k); R := (x, n, k)->p(x, k)^n; f := (t, n, k)->sum(coeff(R(x, n, k), x, j)*(t-1)^j*(n*k-j)!, j=0..n*k); for n from 0 to 6 do seq(coeff(f(t, n, 3), t, m)/3!^n, m=0..3*n); od;
A124009
Number of permutations of n distinct letters (ABCD...) each of which appears thrice with one fixed point.
Original entry on oeis.org
0, 0, 216, 49464, 23123880, 19180338840, 25791442770240, 52614269909090064, 154809621283047068016, 631429039396055199165840, 3457808596178310768284115720, 24763433580060911383347280813320
Offset: 0
1
0, "0", 0, 1
1, "0", 9, 0, 9, 0, 1
56, "216", 378, 435, 324, 189, 54", 27, 0, 1
13833, "49464", 84510, 90944, 69039, 38448, 16476, 5184, 1431, 216, 54, 0, 1
6699824, "23123880", 38358540, 40563765, 30573900, 17399178, 7723640, 2729295, 776520, 180100, 33372, 5355, 540, 90, 0, 1
etc...
-
p := (x, k)->k!^2*sum(x^j/((k-j)!^2*j!), j=0..k); R := (x, n, k)->p(x, k)^n; f := (t, n, k)->sum(coeff(R(x, n, k), x, j)*(t-1)^j*(n*k-j)!, j=0..n*k); for n from 0 to 6 do seq(coeff(f(t, n, 3), t, m)/3!^n, m=0..3*n); od;
A124042
Number of permutations of n distinct letters (ABCD...) each of which appears thrice with two fixed points.
Original entry on oeis.org
0, 9, 378, 84510, 38358540, 31234760055, 41467520432646, 83805898840005132, 244832935610272588920, 993012060508835944545045, 5413243051841698780829328690, 38622438042365626607874252846474
Offset: 0
1
0, 0, "0", 1
1, 0, "9", 0, 9, 0, 1
56, 216, "378", 435, 324, 189, 54", 27, 0, 1
13833, 49464, "84510", 90944, 69039, 38448, 16476, 5184, 1431, 216, 54, 0, 1
6699824, 23123880, "38358540", 40563765, 30573900, 17399178, 7723640, 2729295, 776520, 180100, 33372, 5355, 540, 90, 0, 1
etc...
-
p := (x, k)->k!^2*sum(x^j/((k-j)!^2*j!), j=0..k); R := (x, n, k)->p(x, k)^n; f := (t, n, k)->sum(coeff(R(x, n, k), x, j)*(t-1)^j*(n*k-j)!, j=0..n*k); for n from 0 to 6 do seq(coeff(f(t, n, 3), t, m)/3!^n, m=0..3*n); od;
A124043
Number of permutations of n distinct letters (ABCD...) each of which appears thrice with three fixed points.
Original entry on oeis.org
1, 0, 435, 90944, 40563765, 32659846104, 43036380310735, 86514409614060000, 251739515511526387401, 1017865281673593548065520, 5534999211214597734889370091, 39411238922605740572075832485280
Offset: 0
1
0, 0, 0, "1"
1, 0, 9, "0", 9, 0, 1
56, 216, 378, "435", 324, 189, 54", 27, 0, 1
13833, 49464, 84510, "90944", 69039, 38448, 16476, 5184, 1431, 216, 54, 0, 1
6699824, 23123880, 38358540, "40563765", 30573900, 17399178, 7723640, 2729295, 776520, 180100, 33372, 5355, 540, 90, 0, 1
etc...
-
p := (x, k)->k!^2*sum(x^j/((k-j)!^2*j!), j=0..k); R := (x, n, k)->p(x, k)^n; f := (t, n, k)->sum(coeff(R(x, n, k), x, j)*(t-1)^j*(n*k-j)!, j=0..n*k); for n from 0 to 6 do seq(coeff(f(t, n, 3), t, m)/3!^n, m=0..3*n); od;
A124070
Number of permutations of n distinct letters (ABCD...) each of which appears thrice with 4 fixed points.
Original entry on oeis.org
9, 324, 69039, 30573900, 24571261710, 32346221908896, 64986793207684866, 189028409383462290696, 764111162168487304691175, 4154377697330090433618612780, 29576798800687086868033152117849
Offset: 0
1
0, 0, 0, 1
1, 0, 9, 0, "9", 0, 1
56, 216, 378, 435, "324", 189, 54", 27, 0, 1
13833, 49464, 84510, 90944, "69039", 38448, 16476, 5184, 1431, 216, 54, 0, 1
6699824, 23123880, 38358540, 40563765, "30573900", 17399178, 7723640, 2729295, 776520, 180100, 33372, 5355, 540, 90, 0, 1
etc...
Showing 1-6 of 6 results.