A173296 Numerators of the inverse binomial transform of the Leibniz series for Pi/4.

1, -4, 28, -96, 1328, -4672, 33472, -121856, 3597056, -13417472, 33655808, -127508480, 5829259264, -22308732928, 171393728512, -660468137984, 40831182635008, -22589996269568, 175323994652672, -681560447647744

Offset

0,2

Comments

The series terms for Pi/4 are 1, -1/3, 1/5, -1/7, 1/9, -1/11, + ...

Its inverse binomial transform is 1, -4/3, 28/15, -96/35, 1328/315, -4672/693, + ...

Links

Table of n, a(n) for n=0..19.

Wikipedia, Leibniz series

Maple

L := [seq((-1)^n/(2*n+1), n=0..20)] ;
read("transforms") ; BINOMIALi(L) ;
apply(numer, %) ; # R. J. Mathar, Jul 06 2011

Crossrefs

Cf. A077595, A173294, A001803.

Sequence in context: A263239 A296015 A187452 * A077595 A201243 A092712

Adjacent sequences: A173293 A173294 A173295 * A173297 A173298 A173299

Keyword

frac,sign

Author

Paul Curtz, Feb 15 2010

Extensions

a(3) replaced with reduced numerator and a(5) onwards added by R. J. Mathar, Jul 06 2011

Status

approved