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A228827 Numerators of the first bisection of the inverse binomial transform of the rational sequence with e.g.f. (x/2)*(exp(-x)+1)/(exp(x)-1). 2

%I

%S 1,25,599,4285,15599,169625,33578309,344155,133697983,941417335,

%T 1729982389,3184334285,274574499509,2625798955,1611022490371,

%U 123951819730625,9814145542783,3453861186955,-25128299959971711973,2945661954537595,-260933954573210488051

%N Numerators of the first bisection of the inverse binomial transform of the rational sequence with e.g.f. (x/2)*(exp(-x)+1)/(exp(x)-1).

%C The sequence to be transformed is A176328/A176591, its inverse binomial transform begins: 1, -2, 25/6, -9, 599/30, -45, 4285/42, -231, 15599/30, -1161, 169625/66, -5643, 33578309/2730, ...

%C It appears that a(n) - A000367(n) is a multiple of A002445(n), and the quotients are 0, 4, 20, 102, 520, 2570, 12300, ...

%o (PARI) fr(n) = {default(seriesprecision, n+1); egf = (x/2)*(exp(-x)+1)/(exp(x)-1);(n)!* polcoeff(egf, n);}

%o ibtfr(n) = sum(k = 0, n, (-1)^(n-k)*binomial(n, k) * fr(k));

%o lista(nn) = {forstep(n = 0, nn, 2, print1(numerator(ibtfr(n)), ", "););} \\ _Michel Marcus_, Sep 06 2013

%Y Cf. A228767 (other bisection).

%K frac,sign

%O 0,2

%A _Paul Curtz_ & _Michel Marcus_, Sep 06 2013

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Last modified October 18 05:18 EDT 2019. Contains 328146 sequences. (Running on oeis4.)