A005388 -id:A005388 - cp's OEIS frontend

A053505 Number of degree-n permutations of order dividing 30.

1, 1, 2, 6, 18, 90, 540, 3060, 20700, 145980, 1459800, 13854600, 140059800, 1514748600, 15869034000, 285268878000, 4109761962000, 59488383690000, 935767530036000, 13364309726748000, 240338216104020000, 4540941256642020000, 79739974380153240000

Offset: 0

N. J. A. Sloane, Jan 15 2000

nonn

R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Example 5.2.10.

Alois P. Heinz, Table of n, a(n) for n = 0..200
L. Moser and M. Wyman, On solutions of x^d = 1 in symmetric groups, Canad. J. Math., 7 (1955), 159-168.

Cf. A000085, A001470, A001472, A053495-A053505, A005388.

Column k=30 of A008307.

m:=30; R:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Exp(x +x^2/2 +x^3/3 +x^5/5 +x^6/6 +x^10/10 +x^15/15 +x^30/30) )); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, May 15 2019

a:= proc(n) option remember; `if`(n<0, 0, `if`(n=0, 1,
       add(mul(n-i, i=1..j-1)*a(n-j), j=[1, 2, 3, 5, 6, 10, 15, 30])))
    end:
seq(a(n), n=0..25);  # Alois P. Heinz, Feb 14 2013

a[n_]:= a[n] = If[n<0, 0, If[n==0, 1, Sum[Product[n-i, {i, 1, j-1}]*a[n-j], {j, {1, 2, 3, 5, 6, 10, 15, 30}}]]]; Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Mar 03 2014, after Alois P. Heinz *)
With[{m = 30}, CoefficientList[Series[Exp[x +x^2/2 +x^3/3 +x^5/5 +x^6/6 + x^10/10 +x^15/15 +x^30/30], {x, 0, m}], x]*Range[0, m]!] (* G. C. Greubel, May 15 2019 *)

my(x='x+O('x^30)); Vec(serlaplace( exp(x +x^2/2 +x^3/3 +x^5/5 + x^6/6 +x^10/10 +x^15/15 +x^30/30) )) \\ G. C. Greubel, May 15 2019

m = 30; T = taylor(exp(x +x^2/2 +x^3/3 +x^5/5 +x^6/6 +x^10/10 +x^15/15 +x^30/30), x, 0, m); [factorial(n)*T.coefficient(x, n) for n in (0..m)] # G. C. Greubel, May 15 2019

E.g.f.: exp(x + x^2/2 + x^3/3 + x^5/5 + x^6/6 + x^10/10 + x^15/15 + x^30/30).

A052501 Number of permutations sigma such that sigma^5=Id; degree-n permutations of order dividing 5.

Original entry on oeis.org

1, 1, 1, 1, 1, 25, 145, 505, 1345, 3025, 78625, 809425, 4809025, 20787625, 72696625, 1961583625, 28478346625, 238536558625, 1425925698625, 6764765838625, 189239120970625, 3500701266525625, 37764092547420625, 288099608198025625

Offset: 0

N. J. A. Sloane, Jan 15 2000; encyclopedia(AT)pommard.inria.fr, Jan 25 2000

The number of degree-n permutations of order exactly p (where p is prime) satisfies a(n) = a(n-1) + (1 + a(n-p))*(n-1)!/(n-p)! with a(n)=0 if p>n. Also a(n) = Sum_{j=1..floor(n/p)} (n!/(j!*(n-p*j)!*(p^j))).

These are the telephone numbers T^(5)n of [Artioli et al., p. 7]. - _Eric M. Schmidt, Oct 12 2017

R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Example 5.2.10.

Alois P. Heinz, Table of n, a(n) for n = 0..300
Marcello Artioli, Giuseppe Dattoli, Silvia Licciardi, Simonetta Pagnutti, Motzkin Numbers: an Operational Point of View, arXiv:1703.07262 [math.CO], 2017.
Tomislav Došlic, Darko Veljan, Logarithmic behavior of some combinatorial sequences, Discrete Math. 308 (2008), no. 11, 2182--2212. MR2404544 (2009j:05019). - _N. J. A. Sloane_, May 01 2012
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 26
M. B. Kutler, C. R. Vinroot, On q-Analogs of Recursions for the Number of Involutions and Prime Order Elements in Symmetric Groups, JIS 13 (2010) #10.3.6.
L. Moser and M. Wyman, On solutions of x^d = 1 in symmetric groups, Canad. J. Math., 7 (1955), 159-168.

Cf. A000085, A001470, A001472, A053495-A053505, A005388.

Column k=5 of A008307.

m:=30; R:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Exp(x + x^5/5) )); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, May 14 2019

spec := [S,{S=Set(Union(Cycle(Z,card=1),Cycle(Z,card=5)))},labeled]: seq(combstruct[count](spec,size=n), n=0..20);

max = 30; CoefficientList[ Series[ Exp[x + x^5/5], {x, 0, max}], x]*Range[0, max]! (* Jean-François Alcover, Feb 15 2012, after e.g.f. *)

my(x='x+O('x^30)); Vec(serlaplace( exp(x + x^5/5) )) \\ G. C. Greubel, May 14 2019

m = 30; T = taylor(exp(x + x^5/5), x, 0, m); [factorial(n)*T.coefficient(x, n) for n in (0..m)] # G. C. Greubel, May 14 2019

E.g.f.: exp(x + x^5/5).
a(n+5) = a(n+4) + (24 +50*n +35*n^2 +10*n^3 +n^4)*a(n), with a(0)= ... = a(4) = 1.
a(n) = a(n-1) + a(n-5)*(n-1)!/(n-5)!.
a(n) = Sum_{j = 0..floor(n/5)} n!/(5^j * j! * (n-5*j)!).
a(n) = A059593(n) + 1.

A053496 Number of degree-n permutations of order dividing 6.

Original entry on oeis.org

1, 1, 2, 6, 18, 66, 396, 2052, 12636, 91548, 625176, 4673736, 43575192, 377205336, 3624289488, 38829340656, 397695226896, 4338579616272, 54018173703456, 641634784488288, 8208962893594656, 113809776294348576, 1526808627197721792, 21533423236302943296

Offset: 0

N. J. A. Sloane, Jan 15 2000

nonn

R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Example 5.2.10.

Alois P. Heinz, Table of n, a(n) for n = 0..200
L. Moser and M. Wyman, On solutions of x^d = 1 in symmetric groups, Canad. J. Math., 7 (1955), 159-168.

Cf. A000085, A001470, A001472, A053495-A053505, A005388, A261317.

Column k=6 of A008307.

m:=30; R:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Exp(x + x^2/2 +x^3/3 +x^6/6) )); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, May 14 2019

a:= proc(n) option remember; `if`(n<0, 0, `if`(n=0, 1,
       add(mul(n-i, i=1..j-1)*a(n-j), j=[1, 2, 3, 6])))
    end:
seq(a(n), n=0..25);  # Alois P. Heinz, Feb 14 2013

a[n_] := a[n] = If[n<0, 0, If[n == 0, 1, Sum[Product[n-i, {i, 1, j-1}]*a[n-j], {j, {1, 2, 3, 6}}]]]; Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Mar 03 2014, after Alois P. Heinz *)
With[{m = 30}, CoefficientList[Series[Exp[x +x^2/2 +x^3/3 +x^6/6], {x, 0, m}], x]*Range[0, m]!] (* G. C. Greubel, May 14 2019 *)

my(x='x+O('x^30)); Vec(serlaplace( exp(x+x^2/2+x^3/3+x^6/6) )) \\ G. C. Greubel, May 14 2019

m = 30; T = taylor(exp(x +x^2/2 +x^3/3 +x^6/6), x, 0, m); [factorial(n)*T.coefficient(x, n) for n in (0..m)] # G. C. Greubel, May 14 2019

E.g.f.: exp(x +x^2/2 +x^3/3 +x^6/6).

D-finite with recurrence a(n) -a(n-1) +(-n+1)*a(n-2) -(n-1)*(n-2)*a(n-3) -(n-5)*(n-1)*(n-2)*(n-3)*(n-4)*a(n-6)=0. - R. J. Mathar, Jul 04 2023

A053497 Number of degree-n permutations of order dividing 7.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 721, 5761, 25921, 86401, 237601, 570241, 1235521, 892045441, 13348249201, 106757164801, 604924594561, 2722120577281, 10344007402561, 34479959558401, 24928970490633601, 546446134633639681, 6281586217487489041, 50248618811434961281

Offset: 0

N. J. A. Sloane, Jan 15 2000

nonn

R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Example 5.2.10.

Alois P. Heinz, Table of n, a(n) for n = 0..200
L. Moser and M. Wyman, On solutions of x^d = 1 in symmetric groups, Canad. J. Math., 7 (1955), 159-168.

Sequences with e.g.f. exp(x + x^m/m): A000079 (m=1), A000085 (m=2), A001470 (m=3), A118934 (m=4), A052501 (m=5), A293588 (m=6), this sequence (m=7).
Cf. A000085, A001470, A001472, A005388, A053495 - A053505, A261427.
Column k=7 of A008307.

R:=PowerSeriesRing(Rationals(), 31); Coefficients(R!(Laplace( Exp(x + x^7/7) ))); // G. C. Greubel, May 14 2019, Mar 07 2021

a:= proc(n) option remember; `if`(n<0, 0, `if`(n=0, 1,
       add(mul(n-i, i=1..j-1)*a(n-j), j=[1, 7])))
    end:
seq(a(n), n=0..25); # Alois P. Heinz, Feb 14 2013

CoefficientList[Series[Exp[x+x^7/7], {x, 0, 24}], x]*Range[0, 24]! (* Jean-François Alcover, Mar 24 2014 *)

my(x='x+O('x^30)); Vec(serlaplace( exp(x+x^7/7) )) \\ G. C. Greubel, May 14 2019

f=factorial; [sum(f(n)/(7^j*f(j)*f(n-7*j)) for j in (0..n/7)) for n in (0..30)] # G. C. Greubel, May 14 2019

E.g.f.: exp(x + x^7/7).

a(n) = Sum_{k=0..floor(n/7)} n!/(7^k*k!*(n-7*k)!). - G. C. Greubel, Mar 07 2021

A053499 Number of degree-n permutations of order dividing 9.

Original entry on oeis.org

1, 1, 1, 3, 9, 21, 81, 351, 1233, 46089, 434241, 2359611, 27387801, 264333213, 1722161169, 16514298711, 163094452641, 1216239520401, 50883607918593, 866931703203699, 8473720481213481, 166915156382509221, 2699805625227141201, 28818706120636531023, 439756550972215638129, 6766483260087819272601, 77096822666547068590401, 3568144263578808757678251

Offset: 0

N. J. A. Sloane, Jan 15 2000

nonn

Differs from A218003 first at n=27. - Alois P. Heinz, Jan 25 2014

R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Example 5.2.10.

Alois P. Heinz, Table of n, a(n) for n = 0..200
L. Moser and M. Wyman, On solutions of x^d = 1 in symmetric groups, Canad. J. Math., 7 (1955), 159-168.

Cf. A000085, A001470, A001472, A053495-A053505, A005388, A261429.

Column k=9 of A008307.

m:=30; R:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Exp(x + x^3/3 + x^9/9) )); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, May 15 2019

a:= proc(n) option remember; `if`(n<0, 0, `if`(n=0, 1,
       add(mul(n-i, i=1..j-1)*a(n-j), j=[1, 3, 9])))
    end:
seq(a(n), n=0..25);  # Alois P. Heinz, Feb 14 2013

CoefficientList[Series[Exp[x+x^3/3+x^9/9], {x, 0, 30}], x]*Range[0, 30]! (* Jean-François Alcover, Mar 24 2014 *)

my(x='x+O('x^30)); Vec(serlaplace( exp(x + x^3/3 + x^9/9) )) \\ G. C. Greubel, May 15 2019

m = 30; T = taylor(exp(x + x^3/3 + x^9/9), x, 0, m); [factorial(n)*T.coefficient(x, n) for n in (0..m)] # G. C. Greubel, May 15 2019

E.g.f.: exp(x + x^3/3 + x^9/9).

A053502 Number of degree-n permutations of order dividing 12.

Original entry on oeis.org

1, 1, 2, 6, 24, 96, 576, 3312, 21456, 152784, 1237536, 9984096, 133494912, 1412107776, 16369357824, 206123325696, 2866280276736, 36809077162752, 592066290710016, 8800038127378944, 136876273991755776, 2197453620220010496, 37915306084793106432

Offset: 0

N. J. A. Sloane, Jan 15 2000

nonn

R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Example 5.2.10.

Alois P. Heinz, Table of n, a(n) for n = 0..200
L. Moser and M. Wyman, On solutions of x^d = 1 in symmetric groups, Canad. J. Math., 7 (1955), 159-168.

Cf. A000085, A001470, A001472, A053495-A053505, A005388.

Column k=12 of A008307.

m:=30; R:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Exp(x + x^2/2 + x^3/3 + x^4/4 + x^6/6 + x^12/12) )); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, May 15 2019

a:= proc(n) option remember; `if`(n<0, 0, `if`(n=0, 1,
       add(mul(n-i, i=1..j-1)*a(n-j), j=[1, 2, 3, 4, 6, 12])))
    end:
seq(a(n), n=0..25); # Alois P. Heinz, Feb 14 2013

a[n_]:= a[n] = If[n<0, 0, If[n==0, 1, Sum[Product[n-i, {i, 1, j-1}]*a[n-j], {j, {1, 2, 3, 4, 6, 12}}]]]; Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Apr 24 2014, after Alois P. Heinz *)
With[{m = 30}, CoefficientList[Series[Exp[x +x^2/2 +x^3/3 +x^4/4 +x^6/6 + x^12/12], {x, 0, m}], x]*Range[0, m]!] (* G. C. Greubel, May 15 2019 *)

my(x='x+O('x^30)); Vec(serlaplace( exp(x + x^2/2 + x^3/3 + x^4/4 + x^6/6 + x^12/12) )) \\ G. C. Greubel, May 15 2019

m = 30; T = taylor(exp(x + x^2/2 + x^3/3 + x^4/4 + x^6/6 + x^12/12), x, 0, m); [factorial(n)*T.coefficient(x, n) for n in (0..m)] # G. C. Greubel, May 15 2019

E.g.f.: exp(x + x^2/2 + x^3/3 + x^4/4 + x^6/6 + x^12/12).

A053498 Number of degree-n permutations of order dividing 8.

Original entry on oeis.org

1, 1, 2, 4, 16, 56, 256, 1072, 11264, 78976, 672256, 4653056, 49810432, 433429504, 4448608256, 39221579776, 607251736576, 7244686764032, 101611422797824, 1170362064019456, 19281174853615616, 261583327556386816, 4084459360167657472, 54366023748591386624

Offset: 0

N. J. A. Sloane, Jan 15 2000

nonn

R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Example 5.2.10.

Alois P. Heinz, Table of n, a(n) for n = 0..200
L. Moser and M. Wyman, On solutions of x^d = 1 in symmetric groups, Canad. J. Math., 7 (1955), 159-168.

Cf. A000085, A001470, A001472, A053495-A053505, A005388, A261428.

Column k=8 of A008307.

m:=30; R:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Exp(x +x^2/2 +x^4/4 +x^8/8) )); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, May 14 2019

a:= proc(n) option remember; `if`(n<0, 0, `if`(n=0, 1,
       add(mul(n-i, i=1..j-1)*a(n-j), j=[1, 2, 4, 8])))
    end:
seq(a(n), n=0..25);  # Alois P. Heinz, Feb 14 2013

CoefficientList[Series[Exp[x+x^2/2+x^4/4+x^8/8], {x, 0, 23}], x]*Range[0, 23]! (* Jean-François Alcover, Mar 24 2014 *)

my(x='x+O('x^30)); Vec(serlaplace( exp(x +x^2/2 +x^4/4 +x^8/8) )) \\ G. C. Greubel, May 14 2019

m = 30; T = taylor(exp(x +x^2/2 +x^4/4 +x^8/8), x, 0, m); [factorial(n)*T.coefficient(x, n) for n in (0..m)] # G. C. Greubel, May 14 2019

E.g.f.: exp(x + x^2/2 + x^4/4 + x^8/8).

A053504 Number of degree-n permutations of order dividing 24.

Original entry on oeis.org

1, 1, 2, 6, 24, 96, 576, 3312, 26496, 198144, 1691136, 14973696, 193370112, 2034809856, 25087186944, 313539434496, 4421478721536, 58307347556352, 915011420737536, 13553664911437824, 240637745416421376, 3965015057937924096

Offset: 0

N. J. A. Sloane, Jan 15 2000

nonn

R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Example 5.2.10.

Alois P. Heinz, Table of n, a(n) for n = 0..200
L. Moser and M. Wyman, On solutions of x^d = 1 in symmetric groups, Canad. J. Math., 7 (1955), 159-168.

Cf. A000085, A001470, A001472, A053495-A053505, A005388.

Column k=24 of A008307.

m:=30; R:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Exp(x +x^2/2 +x^3/3 +x^4/4 +x^6/6 +x^8/8 +x^12/12 +x^24/24) )); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, May 15 2019

a:= proc(n) option remember; `if`(n<0, 0, `if`(n=0, 1,
       add(mul(n-i, i=1..j-1)*a(n-j), j=[1, 2, 3, 4, 6, 8, 12, 24])))
    end:
seq(a(n), n=0..25);  # Alois P. Heinz, Jan 25 2014

a[n_]:= a[n] = If[n<0, 0, If[n==0, 1, Sum[Product[n-i, {i, 1, j-1}]*a[n-j], {j, {1, 2, 3, 4, 6, 8, 12, 24}}]]]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Mar 19 2014, after Alois P. Heinz *)
With[{nn=30},CoefficientList[Series[Exp[Total[x^#/#&/@Divisors[24]]],{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Mar 05 2016 *)

N=30; x='x+O('x^N);
Vec(serlaplace(exp(sumdiv(24, d, x^d/d)))) \\ Gheorghe Coserea, May 11 2017

m = 30; T = taylor(exp(x +x^2/2 +x^3/3 +x^4/4 +x^6/6 +x^8/8 +x^12/12 +x^24/24), x, 0, m); [factorial(n)*T.coefficient(x, n) for n in (0..m)] # G. C. Greubel, May 15 2019

E.g.f.: exp(x + x^2/2 + x^3/3 + x^4/4 + x^6/6 + x^8/8 + x^12/12 + x^24/24).

A053500 Number of degree-n permutations of order dividing 10.

Original entry on oeis.org

1, 1, 2, 4, 10, 50, 220, 1240, 6140, 32860, 602200, 5668400, 62030200, 522328600, 4487190800, 62591332000, 715163146000, 9573774122000, 105731659828000, 1187355279592000, 29205778751300000, 481597207656340000, 9086318388933400000, 132525988426667120000

Offset: 0

N. J. A. Sloane, Jan 15 2000

nonn

R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Example 5.2.10.

Alois P. Heinz, Table of n, a(n) for n = 0..200
L. Moser and M. Wyman, On solutions of x^d = 1 in symmetric groups, Canad. J. Math., 7 (1955), 159-168.

Cf. A000085, A001470, A001472, A053495-A053505, A005388.

Column k=10 of A008307.

m:=30; R:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Exp(x + x^2/2 + x^5/5 + x^10/10) )); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, May 15 2019

a:= proc(n) option remember; `if`(n<0, 0, `if`(n=0, 1,
       add(mul(n-i, i=1..j-1)*a(n-j), j=[1, 2, 5, 10])))
    end:
seq(a(n), n=0..25);  # Alois P. Heinz, Feb 14 2013

a[n_]:= a[n] = If[n<0, 0, If[n==0, 1, Sum[Product[n-i, {i, 1, j-1}] *a[n-j], {j, {1, 2, 5, 10}}]]]; Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Apr 24 2014, after Alois P. Heinz *)
With[{m = 30}, CoefficientList[Series[Exp[x +x^2/2 +x^5/5 +x^10/10], {x, 0, m}], x]*Range[0, m]!] (* G. C. Greubel, May 15 2019 *)

my(x='x+O('x^30)); Vec(serlaplace( exp(x + x^2/2 + x^5/5 + x^10/10) )) \\ G. C. Greubel, May 15 2019

m = 30; T = taylor(exp(x + x^2/2 + x^5/5 + x^10/10), x, 0, m); [factorial(n)*T.coefficient(x, n) for n in (0..m)] # G. C. Greubel, May 15 2019

E.g.f.: exp(x + x^2/2 + x^5/5 + x^10/10).

A053501 Number of degree-n permutations of order dividing 11.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3628801, 43545601, 283046401, 1320883201, 4953312001, 15850598401, 44910028801, 115482931201, 274271961601, 609493248001, 1279935820801, 4644633666390681601, 106826520356358566401, 1281918194457262387201

Offset: 0

N. J. A. Sloane, Jan 15 2000

nonn

R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Example 5.2.10.

Alois P. Heinz, Table of n, a(n) for n = 0..200
Vladimir Kruchinin and D. V. Kruchinin, Composita and their properties, arXiv:1103.2582 [math.CO], 2011-2013.
L. Moser and M. Wyman, On solutions of x^d = 1 in symmetric groups, Canad. J. Math., 7 (1955), 159-168.

Cf. A000085, A001470, A001472, A053495-A053505, A005388.

Column k=11 of A008307.

m:=30; R:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Exp(x + x^11/11) )); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, May 15 2019

a:= proc(n) option remember; `if`(n<0, 0, `if`(n=0, 1,
       add(mul(n-i, i=1..j-1)*a(n-j), j=[1, 11])))
    end:
seq(a(n), n=0..30);  # Alois P. Heinz, Feb 14 2013

a[n_]:= n!*Sum[If[Mod[11*k-n, 10] == 0, Binomial[k, (11*k-n)/10]*11^((k-n)/10)/k!, 0], {k, 1, n}]; a[0] = 1; Table[a[n], {n, 0, 24}] (* Jean-François Alcover, Mar 20 2014, after Vladimir Kruchinin *)
With[{m = 30}, CoefficientList[Series[Exp[x +x^11/11], {x, 0, m}], x]*Range[0, m]!] (* G. C. Greubel, May 15 2019 *)

a(n):=n!*sum(if mod(11*k-n,10)=0 then binomial(k,(11*k-n)/10)*(11)^((k-n)/10)/k! else 0,k,1,n); /* Vladimir Kruchinin, Sep 10 2010 */

my(x='x+O('x^30)); Vec(serlaplace( exp(x +x^11/11) )) \\ G. C. Greubel, May 15 2019

m = 30; T = taylor(exp(x +x^11/11), x, 0, m); [factorial(n)*T.coefficient(x, n) for n in (0..m)] # G. C. Greubel, May 15 2019

E.g.f.: exp(x + x^11/11).

a(n) = n!*Sum_{k=1..n} (if mod(11*k-n,10)=0 then C(k,(11*k-n)/10)*(11)^((k-n)/10)/k!, else 0), n>0. - Vladimir Kruchinin, Sep 10 2010

cp's OEIS Frontend

A053505 Number of degree-n permutations of order dividing 30.

Views

Author

Keywords

References

Links

Crossrefs

Programs

Magma

Maple

Mathematica

PARI

Sage

Formula

A052501 Number of permutations sigma such that sigma^5=Id; degree-n permutations of order dividing 5.

Views

Author

Keywords

Comments

References

Links

Crossrefs

Programs

Magma

Maple

Mathematica

PARI

Sage

Formula

A053496 Number of degree-n permutations of order dividing 6.

Views

Author

Keywords

References

Links

Crossrefs

Programs

Magma

Maple

Mathematica

PARI

Sage

Formula

A053497 Number of degree-n permutations of order dividing 7.

Views

Author

Keywords

References

Links

Crossrefs

Programs

Magma

Maple

Mathematica

PARI

Sage

Formula

A053499 Number of degree-n permutations of order dividing 9.

Views

Author

Keywords

Comments

References

Links

Crossrefs

Programs

Magma

Maple

Mathematica

PARI

Sage

Formula

A053502 Number of degree-n permutations of order dividing 12.

Views

Author

Keywords

References

Links

Crossrefs