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Triangle read by rows: coefficients for step-by-step integration.
12

%I #18 Oct 03 2021 22:24:32

%S 1,3,-1,23,-16,5,165,-177,111,-27,3802,-5548,5232,-2548,502,21385,

%T -39615,49910,-36490,14385,-2375,993605,-2235440,3527745,-3441280,

%U 2035695,-672360,95435

%N Triangle read by rows: coefficients for step-by-step integration.

%H W. F. Pickard, <a href="https://doi.org/10.1145/321217.321226">Tables for the step-by-step integration of ordinary differential equations of the first order</a>, J. ACM 11 (1964), 229-233.

%H W. F. Pickard, <a href="/A002397/a002397.pdf">Tables for the step-by-step integration of ordinary differential equations of the first order</a>, J. ACM 11 (1964), 229-233. [Annotated scanned copy] See Table II.

%e Triangle begins:

%e 1;

%e 3, -1;

%e 23, -16, 5;

%e 165, -177, 111, -27;

%e 3802, -5548, 5232, -2548, 502;

%e ...

%Y Row sums = A002397.

%Y Diagonals (up to signs in some cases) include A002398, A002399, A002400, A002401, A002404.

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

%K sign,tabl,more

%O 0,2

%A _N. J. A. Sloane_, Aug 02 2015

%E a(15)-a(27) from _Robert Price_, Sep 09 2019