OFFSET
0,3
COMMENTS
These are the coefficients of the n-th forward difference of f in the estimate for y(x1) - y(x0), also the coefficients of f(x0) in the estimate for 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 this sequence is 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+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
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Sean A. Irvine, Nov 10 2013
More terms from Jack W Grahl, Feb 28 2021
STATUS
approved