A002404 Coefficients for step-by-step integration.

3, -16, 111, -2548, 14385, -672360, 10351845, -270594968, 2631486186, -310710613080, 3648232023975, -604596371658444, 8315244191734623, -122717408718016112, 3868618892876082345, -1102643727493413977872, 19593301788429800483052, -6988461512994426036295152, 138198195880599649938536250

Offset: 0

Author

N. J. A. Sloane

Keywords

• sign

Comments

These are the coefficients of f(x_{-n}) in the estimate for y(x1) - y(x0) which has n + 1 terms.

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]

Crossrefs

If every other term is negated, this is a diagonal of A260780.

The following sequences are taken from page 231 of Pickard (1964): A002397, A002398, A002399, A002400, A002401, A002402, A002403, A002404, A002405, A002406, A260780, A260781.

Extensions

More terms from Jack W Grahl, Feb 28 2021