A002701 Coefficients for numerical differentiation.

1, 1, 7, 41, 479, 59, 266681, 63397, 514639, 178939, 10410343, 18500393, 40799043101, 1411432849, 6620481151, 48409924397, 238357395880861, 339716530787, 86364397717734821, 421950627598601, 222226462279, 15392144025383

Offset: 2

Author

N. J. A. Sloane

Keywords

• nonn
• frac

References

• 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

• H. E. Salzer, Coefficients for numerical differentiation with central differences, J. Math. Phys., 22 (1943), 115-135.
• H. E. Salzer, Coefficients for numerical differentiation with central differences, J. Math. Phys., 22 (1943), 115-135. [Annotated scanned copy]
• T. R. Van Oppolzer, Lehrbuch zur Bahnbestimmung der Kometen und Planeten, Vol. 2, Engelmann, Leipzig, 1880, p. 21 (see numerators of numbers named N(3,2k+1) and N(4,2k)).

Crossrefs

Cf. A002455 (central factorial numbers), A002702 (denominators).

Formula

a(n) = numer(6 * A002455(n) / 2^(2*n) * (2*n + 3)!). - Sean A. Irvine, Jun 10 2014

Extensions

More terms from Sean A. Irvine, Jun 10 2014