A001238 Differences of reciprocals of unity. (Formerly M5328 N2316)

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

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

Table of n, a(n) for n=1..10.

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

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

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 *)

Prog

(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

Crossrefs

Column 5 in triangle A008969.

Sequence in context: A177233 A183482 A327416 * A230183 A183552 A210824

Adjacent sequences: A001235 A001236 A001237 * A001239 A001240 A001241

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Sean A. Irvine, Mar 29 2012

Status

approved