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).

1, 25, 599, 4285, 15599, 169625, 33578309, 344155, 133697983, 941417335, 1729982389, 3184334285, 274574499509, 2625798955, 1611022490371, 123951819730625, 9814145542783, 3453861186955, -25128299959971711973, 2945661954537595, -260933954573210488051

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