A002702 Coefficients for numerical differentiation. (Formerly M3709 N1515)

1, 4, 120, 3024, 151200, 79200, 1513512000, 1513512000, 51459408000, 74662922880, 18068427336960, 133196739984000, 1215553449093984000, 173650492727712000, 3357242859402432000, 101013513093196704000, 2043503369875369321920000

Offset

2,2

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..18.

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 denominators of numbers named N(3,2k+1)).

Formula

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

Crossrefs

Cf. A002455 (central factorial numbers), A002701 (numerators).

Sequence in context: A006434 A240397 A347425 * A068204 A203033 A307935

Adjacent sequences: A002699 A002700 A002701 * A002703 A002704 A002705

Keyword

nonn,frac

Author

N. J. A. Sloane

Extensions

More terms from Sean A. Irvine, Jun 10 2014

Status

approved