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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
 1, 25, 599, 4285, 15599, 169625, 33578309, 344155, 133697983, 941417335, 1729982389, 3184334285, 274574499509, 2625798955, 1611022490371, 123951819730625, 9814145542783, 3453861186955, -25128299959971711973, 2945661954537595, -260933954573210488051 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS 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, ... It appears that a(n) - A000367(n) is a multiple of A002445(n), and the quotients are 0, 4, 20, 102, 520, 2570, 12300, ... LINKS Table of n, a(n) for n=0..20. PROG (PARI) fr(n) = {default(seriesprecision, n+1); egf = (x/2)*(exp(-x)+1)/(exp(x)-1); (n)!* polcoeff(egf, n); } ibtfr(n) = sum(k = 0, n, (-1)^(n-k)*binomial(n, k) * fr(k)); lista(nn) = {forstep(n = 0, nn, 2, print1(numerator(ibtfr(n)), ", "); ); } \\ Michel Marcus, Sep 06 2013 CROSSREFS Cf. A228767 (other bisection). Sequence in context: A014909 A239822 A264220 * A159661 A104643 A162811 Adjacent sequences: A228824 A228825 A228826 * A228828 A228829 A228830 KEYWORD frac,sign AUTHOR Paul Curtz & Michel Marcus, Sep 06 2013 STATUS approved

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Last modified June 17 10:05 EDT 2024. Contains 373445 sequences. (Running on oeis4.)