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Numerators of the inverse binomial transform of the Leibniz series for Pi/4.
2

%I #10 Feb 25 2019 08:22:04

%S 1,-4,28,-96,1328,-4672,33472,-121856,3597056,-13417472,33655808,

%T -127508480,5829259264,-22308732928,171393728512,-660468137984,

%U 40831182635008,-22589996269568,175323994652672,-681560447647744

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

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

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

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Leibniz_series">Leibniz series</a>

%p L := [seq((-1)^n/(2*n+1),n=0..20)] ;

%p read("transforms") ; BINOMIALi(L) ;

%p apply(numer,%) ; # _R. J. Mathar_, Jul 06 2011

%Y Cf. A077595, A173294, A001803.

%K frac,sign

%O 0,2

%A _Paul Curtz_, Feb 15 2010

%E a(3) replaced with reduced numerator and a(5) onwards added by _R. J. Mathar_, Jul 06 2011