A002686 Coefficients for numerical integration.

1, 8, 45, 416, 1685, 31032, 1603182, 13856896, 132843888, 6551143600

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Comments

From Petros Hadjicostas, Oct 29 2019: (Start)

This is the secondary main diagonal of A324124 (which is essentially Table I on p. 217 in Luke (1952)), except that a(7) = 1603182 must be replaced with 1603182/7 = 229026. This is necessary to give a unique definition to the terms of A324124. For more information, see the comments for A324124.

Luke (1952) is not wrong (since 1603182/4054050 = 229026/579150), but his integers for the case n = 7 have to modified as mentioned in the documentation of array A324124. For an improved version of this sequence, see A328885. (End)

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

• Yudell L. Luke, Mechanical quadrature near a singularity, Math. Comp. 6 (1952), 215-219.

Crossrefs

Cf. A002685, A328866, A328884, A328885.

Secondary diagonal of A324124 (except for a(7)).