OFFSET
0,4
COMMENTS
All the terms except the first term are negative. - Sean A. Irvine, Nov 10 2013
a(n) / A002397(n) is the coefficient of the n-th forward difference of f in the estimate of y(x0) - y(x1).
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
Jack W Grahl, Table of n, a(n) for n = 0..100
Jack W Grahl, Explanation of how the sequence was calculated
Jack W Grahl, Python code to calculate this and related sequences
W. F. Pickard, Tables for the step-by-step integration of ordinary differential equations of the first order, J. ACM 11 (1964), 229-233.
W. F. Pickard, Tables for the step-by-step integration of ordinary differential equations of the first order, J. ACM 11 (1964), 229-233. [Annotated scanned copy]
FORMULA
a(n) = lcm{1,2,...,n+1} * Sum_{k=0..n}((-1)^(n-k)/n+1-k)*s(-(n-1),k,n) where s(l,m,n) are the generalized Stirling numbers of the first kind. - Sean A. Irvine, Nov 10 2013
CROSSREFS
With different signs, this is the leading diagonal of A260781.
The coefficients used in numerical integration are given by fractions with A002397 as the denominators.
A002401 is the corresponding sequence for the symmetric method of estimation.
KEYWORD
sign
AUTHOR
EXTENSIONS
More terms from Sean A. Irvine, Nov 10 2013
More terms from Jack W Grahl, Feb 28 2021
STATUS
approved