OFFSET
1,1
REFERENCES
F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 228.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..70
Mircea Merca, Some experiments with complete and elementary symmetric functions, Periodica Mathematica Hungarica, 69 (2014), 182-189.
FORMULA
a(n) = (n+1)!^3 * Sum_{i=1..n+1} Sum_{j=1..i} Sum_{k=1..j} 1/(i*j*k).
From Vladeta Jovovic, Jan 30 2005: (Start)
a(n) = (n!^3/6)*(H(n, 1)^3+3*H(n, 1)*H(n, 2)+2*H(n, 3)), where H(n, m) = Sum_{i=1..n} 1/i^m are generalized harmonic numbers.
a(n) = (n!^3/6)*((Psi(n+1)+gamma)^3+3*(Psi(n+1)+gamma)*(-Psi(1, n+1)+1/6*Pi^2)+Psi(2, n+1)+2*Zeta(3)).
a(n) = n!^3*Sum_{k=1..n} (-1)^(k+1)*binomial(n, k)/k^3.
Sum_{n>=0} a(n)*x^n/n!^3 = polylog(3, x/(x-1))/(x-1). (offset 2). (End)
MAPLE
a:= n-> (n+1)!^3* add((-1)^(k+1) *binomial(n+1, k)/ k^3, k=1..n+1):
seq (a(n), n=1..15); # Alois P. Heinz, Sep 05 2008
MATHEMATICA
h = HarmonicNumber; a[n_] := ((n+1)!^3/6)*(h[n+1, 1]^3 + 3*h[n+1, 1]*h[n+1, 2] + 2*h[n+1, 3]); Table[a[n], {n, 1, 15}] (* Jean-François Alcover, Feb 26 2015, after Vladeta Jovovic *)
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Alois P. Heinz, Sep 05 2008
STATUS
approved