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A002401
Coefficients for step-by-step integration.
(Formerly M3947 N1626)
12
1, 1, 5, 27, 502, 2375, 95435, 1287965, 29960476, 262426878, 28184365650, 303473091075, 46437880787562, 593196287807409, 8172332906336599, 241563260379065625, 64808657541894257992, 1087738506483388123364, 367580830209839294339148, 6906008426663826491899602, 136666305828261517346022452
OFFSET
0,3
COMMENTS
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).
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).
FORMULA
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
CROSSREFS
Column 0 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.
Sequence in context: A360732 A135627 A244655 * A034946 A321072 A119941
KEYWORD
nonn
EXTENSIONS
More terms from Sean A. Irvine, Nov 10 2013
More terms from Jack W Grahl, Feb 28 2021
STATUS
approved