A002401 - OEIS

%I M3947 N1626 #31 Jan 05 2022 00:10:31

%S 1,1,5,27,502,2375,95435,1287965,29960476,262426878,28184365650,

%T 303473091075,46437880787562,593196287807409,8172332906336599,

%U 241563260379065625,64808657541894257992,1087738506483388123364,367580830209839294339148,6906008426663826491899602,136666305828261517346022452

%N Coefficients for step-by-step integration.

%C These are the coefficients of the n-th forward difference of f in the estimate for y(x1) - y(x0), also the coefficients of f(x0) in the estimate for y(x0) - y(x1).

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Jack W Grahl, <a href="/A002401/b002401.txt">Table of n, a(n) for n = 0..100</a>

%H Jack W Grahl, <a href="/A002405/a002405.pdf">Explanation of how this sequence is calculated</a>

%H Jack W Grahl, <a href="/A002405/a002405.py.txt">Python code to calculate this and related sequences</a>

%H W. F. Pickard, <a href="http://dx.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]

%F a(n) = lcm{1,2,...,n+1} * Sum_{k=0..n}(1/n+1-k)*s(-(n-1),k,n) where s(l,m,n) are the generalized Stirling numbers of the first kind. - _Sean A. Irvine_, Nov 10 2013

%Y Column 0 of A260781.

%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 nonn

%O 0,3

%A _N. J. A. Sloane_

%E More terms from _Sean A. Irvine_, Nov 10 2013

%E More terms from _Jack W Grahl_, Feb 28 2021