A000424 Differences of reciprocals of unity. (Formerly M4448 N1883)

7, 85, 1660, 48076, 1942416, 104587344, 7245893376, 628308907776, 66687811660800, 8506654697548800, 1284292319599411200, 226530955276874956800, 46165213716463676620800, 10765453901922078105600000, 2848453606917036402278400000, 848800150518516674081587200000

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..16.

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

Formula

From Vaclav Kotesovec, Oct 23 2017: (Start)

a(n) = (3*n^2 + 3*n + 1)*a(n-1) - 3*n^4*a(n-2) + (n-1)^3*n^3*a(n-3).

a(n) ~ Pi * log(n)^2 * n^(2*n + 3) * (1 + 2*gamma/log(n) + (gamma^2 + Pi^2/6) / log(n)^2) / exp(2*n), where gamma is the Euler-Mascheroni constant (A001620). (End)

Mathematica

T[n_, k_] := If[k <= n, (n-k+2)!^k*Sum[(-1)^(j+1)*Binomial[n-k+2, j]/j^k, {j, 1, n-k+2}], 0]; a[n_] := T[n+1, 2]; Table[a[n], {n, 1, 10}] (* Jean-François Alcover, Feb 08 2016, after Alois P. Heinz in A008969 *)

Crossrefs

Essentially the same as A060237.

Column 2 in triangle A008969.

Sequence in context: A363357 A121020 A060237 * A368787 A207214 A000686

Adjacent sequences: A000421 A000422 A000423 * A000425 A000426 A000427

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Vaclav Kotesovec, Oct 23 2017

Status

approved