A002551 Numerators of coefficients in Taylor series expansion of log(1+x)^2/sqrt(1+x).

0, 1, -3, 43, -95, 12139, -25333, 81227, -498233, 121563469, -246183839, 32808117961, -13219717433, 3226018634857, -8835766426243, 390013167515221, -260612031438103, 36514732926665911, -73104960503491573, 9265088297941326563, -389193444786378151123

Offset: 1

Author

N. J. A. Sloane

Keywords

• sign
• frac

Comments

Old title: Numerators of coefficients for numerical differentiation.

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

• 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).
• W. G. Bickley and J. C. P. Miller, Numerical differentiation near the limits of a difference table. [Annotated scanned copy]

Crossrefs

Cf. A002552.

Programs

PARI

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

Extensions

More terms from Sean A. Irvine, Mar 24 2014

Signs from Michel Marcus, Oct 31 2014