A001242 Differences of reciprocals of unity.

1, 274, 48076, 6998824, 929081776, 117550462624, 14500866102976, 1765130436471424, 213373597575314176, 25700650466807540224, 3089923562153380965376, 371145495540181143169024, 44558899569395347436056576, 5348360831598738338465357824

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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

• Colin Barker, Table of n, a(n) for n = 1..481
• Mircea Merca, Some experiments with complete and elementary symmetric functions, Periodica Mathematica Hungarica, 69 (2014), 182-189.
• Index entries for linear recurrences with constant coefficients, signature (274,-27000,1224000,-25920000,207360000).

Crossrefs

Equals 2^(n-1) * A103878(n).

Right-hand column 4 in triangle A008969.

Cf. a(n) = A112492(n+3, 5).

Programs

PARI

Vec(1/(-207360000*x^5+25920000*x^4-1224000*x^3+27000*x^2-274*x+1) + O(x^100)) \\ Colin Barker, Apr 26 2015

Formula

G.f.: x / ((1-24*x)*(1-30*x)*(1-40*x)*(1-60*x)*(1-120*x)).

a(n) = (1/24) (24^n - 4*30^n + 6*40^n - 4*60^n + 120^n).

Extensions

Formulae and more terms from Ralf Stephan, Feb 20 2005