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A001236 Differences of reciprocals of unity.
(Formerly M4993 N2149)
2
15, 575, 46760, 6998824, 1744835904, 673781602752, 381495483224064, 303443622431870976, 327643295527342080000, 466962174913357393920000, 858175477913267353681920000, 1993920215002599923346309120000, 5758788816015998806424467537920000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

REFERENCES

F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 228.

M. Merca, Some experiments with complete and elementary symmetric functions, - Periodica Mathematica Hungarica, 69 (2014), 182-189.

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

FORMULA

(n+1)!^3 * Sum[i=1..n+1, Sum[j=1..i, Sum[k=1..j, 1/(ijk) ]]].

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) - Vladeta Jovovic, Jan 30 2005

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-Fran├žois Alcover, Feb 26 2015, after Vladeta Jovovic *)

CROSSREFS

Column 3 in triangle A008969.

Cf. A000254, A000424, A001237, A001238.

Sequence in context: A027462 A329122 A027534 * A263887 A183546 A179895

Adjacent sequences:  A001233 A001234 A001235 * A001237 A001238 A001239

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Alois P. Heinz, Sep 05 2008

STATUS

approved

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Last modified November 15 13:47 EST 2019. Contains 329149 sequences. (Running on oeis4.)