A002701 Coefficients for numerical differentiation. (Formerly M4424 N1870)

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

Offset

2,3

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

Table of n, a(n) for n=2..23.

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)).

Formula

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

Crossrefs

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

Sequence in context: A377347 A356129 A053676 * A057006 A144747 A176090

Adjacent sequences: A002698 A002699 A002700 * A002702 A002703 A002704

Keyword

nonn,frac

Author

N. J. A. Sloane

Extensions

More terms from Sean A. Irvine, Jun 10 2014

Status

approved