OFFSET
0,3
REFERENCES
R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Example 5.2.10.
LINKS
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.
FORMULA
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).
MAPLE
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
MATHEMATICA
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 *)
PROG
(PARI) 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
(Magma) m:=30; R<x>:=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
(Sage) 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
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jan 15 2000
STATUS
approved