A002399 Coefficients for step-by-step integration. (Formerly M5015 N2160)

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

Offset

1,2

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.

Sequence in context: A323856 A226507 A264297 * A255255 A181239 A021084

Adjacent sequences: A002396 A002397 A002398 * A002400 A002401 A002402

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Jack W Grahl, Feb 28 2021

Status

approved