A002399 Coefficients for step-by-step integration.

1, 16, 177, 5548, 39615, 2236440, 40325915, 1207505768, 13229393814, 1737076976040, 22446050738265, 4058838484620084, 60476452041557409, 961082989270516112, 32455938583801467735, 9864953815464307351792, 186195769473110823077652, 70295408103581008790661648, 1466826914074651870368663750

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Comments

These are the negated coefficients of f(x_{-1}) in the estimate for y(x1) - y(x0).

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 = 1..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]

Crossrefs

Column 1 (negated) 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