The On-Line Encyclopedia of Integer Sequences (OEIS)

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A002551

Numerators of coefficients in Taylor series expansion of log(1+x)^2/sqrt(1+x).
(history; published version)

#19 by Michel Marcus at Fri Oct 31 05:34:57 EDT 2014

STATUS

editing

proposed

Discussion

Fri Oct 31

06:51

Joerg Arndt: I suggest to put the signs in.

#18 by Michel Marcus at Fri Oct 31 05:34:18 EDT 2014

PROG

(PARI) a(n) = default(seriesprecision, n); numerator(polcoeff(Pol(log(1+x)^2/sqrt(1+x) + O(x^(2*n))), n)); \\ Michel Marcus, Oct 31 2014

Discussion

Fri Oct 31

05:34

Michel Marcus: I find same terms but signed:
0, 1, -3, 43, -95, 12139, -25333, 81227, -498233, 121563469, -246183839,

#17 by Michel Marcus at Fri Oct 31 05:15:17 EDT 2014

REFERENCES

W. G. Bickley and J. C. P. Miller, Numerical differentiation near the limits of a difference table, Phil. Mag., 33 (1942), 1-12 (plus tables).

LINKS

W. G. Bickley and J. C. P. Miller, <a href="http://dx.doi.org/10.1080/14786444208521334">Numerical differentiation near the limits of a difference table</a>, Phil. Mag., 33 (1942), 1-12 (plus tables).

#16 by Michel Marcus at Fri Oct 31 05:14:17 EDT 2014

KEYWORD

nonn,frac

STATUS

approved

editing

#15 by N. J. A. Sloane at Tue Mar 25 00:10:37 EDT 2014

STATUS

editing

approved

#14 by N. J. A. Sloane at Tue Mar 25 00:10:35 EDT 2014

NAME

Numerators of coefficients of in Taylor series expansion of log(1+x)^2/sqrt(1+x).

STATUS

approved

editing

#13 by N. J. A. Sloane at Tue Mar 25 00:08:46 EDT 2014

STATUS

editing

approved

#12 by N. J. A. Sloane at Tue Mar 25 00:06:45 EDT 2014

NAME

Numerators of coefficients of Taylor series expansion of log(1+x)^2/sqrt(1+x).

COMMENTS

Old title: Numerators of coefficients for numerical differentiation.

STATUS

proposed

editing

Discussion

Tue Mar 25

00:08

N. J. A. Sloane: I actually like the old title, since it has been there since about 1970 when I was working on the 1973 book. So I'm preserving it as a comment.
Also I added the missing phrase Taylor series ... to the definition!

#11 by Sean A. Irvine at Mon Mar 24 22:21:19 EDT 2014

STATUS

editing

proposed

#10 by Sean A. Irvine at Mon Mar 24 22:21:00 EDT 2014

NAME

Numerators of coefficients for numerical differentiationof log(1+x)^2/sqrt(1+x).

DATA

0, 1, 3, 43, 95, 12139, 25333, 81227, 498233, 121563469, 246183839, 32808117961, 13219717433, 3226018634857, 8835766426243, 390013167515221, 260612031438103, 36514732926665911, 73104960503491573, 9265088297941326563

OFFSET

1,23

EXTENSIONS

More terms from Sean A. Irvine, Mar 24 2014

STATUS

approved

editing