A176618 The numerator of the n-th term of the inverse binomial transform of the sequence 0, 1, 0, B_2, B_3, B_4, .. of modified Bernoulli numbers.

0, 1, -2, 19, -14, 199, -137, 851, -548, 4121, -2533, 67451, -40078, 404869, -234967, 1655047, -940136, 32428087, -18383711, 439693871, -235204778, -724823111, 352226881, 260572074487, -130542594044, -6002444699183, 3000757572779

Offset: 0

Author

Paul Curtz, Apr 22 2010

Keywords

• frac
• sign

Comments

The starting sequence contains the terms A176327(.)/A176591(.) prefixed with a single zero (which occupies the term at index zero), basically 0, 1, 0 followed by the Bernoulli numbers without B_0 and B_1.

Its inverse binomial transform is 0, 1, -2, 19/6, -14/3, 199/30, -137/15, 851/70, -548/35, 4121/210, -2533/105, 67451/2310, -40078/1155, 404869/10010, -234967/5005, 1655047/30030,.. and taking numerators defines the current sequence.

The denominators of the transformed sequence appear to be A172031, checked up to A176618(33).

Programs

Maple

read("transforms") ;
evb := [0, 1, 0, seq(bernoulli(n), n=2..50)] ;
ievb := BINOMIALi(evb) ;
apply(numer,%) ;