A001238 Differences of reciprocals of unity.

63, 22631, 30480800, 117550462624, 1083688832185344, 21006340945438768128, 778101042571221893382144, 51150996584622542869024997376, 5626686079269855254796985958400000, 987233834003503822099304377378406400000

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

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

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

Crossrefs

Column 5 in triangle A008969.

Programs

Mathematica

a[n_] := -(Factorial[n + 1]^5)*Sum[(-1)^k Binomial[n + 1, k]/k^5, {k, 1, n + 1}];Table[a[n],{n,10}] (* James C. McMahon, Dec 12 2023 *)

PARI

a(n) = (n+1)!^5 * sum(k=1, n+1, (-1)^(k+1)*binomial(n+1,k)/k^5); \\ Michel Marcus, Apr 28 2020

Formula

a(n) = (n+1)!^5 * Sum_{k=1..n+1} ((-1)^(k+1)*C(n+1,k)/k^5). - Sean A. Irvine, Mar 30 2012; corrected by Michel Marcus, Apr 28 2020

Extensions

More terms from Sean A. Irvine, Mar 29 2012