A002686 - OEIS

A002686

Coefficients for numerical integration.
(Formerly M4533 N1922)

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

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OFFSET

1,2

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

Table of n, a(n) for n=1..10.

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)).

Sequence in context: A009369 A120044 A328885 * A306047 A110348 A336999

Adjacent sequences: A002683 A002684 A002685 * A002687 A002688 A002689

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

STATUS

approved