A002685 Coefficients for numerical integration. (Formerly M1702 N0671)

2, 6, 34, 250, 972, 15498, 766808, 5961306, 54891535, 2488870076

Offset

1,1

Comments

From Petros Hadjicostas, Oct 29 2019: (Start)

This is the main diagonal of A324124 (which is essentially the table on p. 217 in Luke (1952)), except that a(7) = 766808 must be replaced with 766808/7 = 109544. 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 766808/4054050 = 109544/579150), 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 A328884. (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. A002686, A328866, A328884, A328885.

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

Sequence in context: A108424 A364394 A328884 * A262391 A271212 A325296

Adjacent sequences: A002682 A002683 A002684 * A002686 A002687 A002688

Keyword

nonn

Author

N. J. A. Sloane

Status

approved