A002406 Coefficients for step-by-step integration.

1, 8, -15, 212, -865, 31560, -397285, 8760472, -73512810, 7619823960, -79612742055, 11869626289356, -148201090063455, 2000757995572336, -58073355854498985, 15325818191986269968, -253388757170439526636, 84454267865884467099120, -1566608640281391343515450, 30637801046762651850275960

Offset: 0

Author

N. J. A. Sloane

Keywords

• sign

Comments

These are the coefficients of f(x_{-n}) in the estimate for y(x0) - y(x1) which has n + 2 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

Second diagonal of A260781.

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