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A176150 Numerators of the inverse binomial transform of a shuffled sequence of "original" Bernoulli and Bernoulli numbers. 3
1, 0, -1, 0, 13, -20, 14, -73, 373, -776, 196, -223, 1027, -1956, 242, 139, -3521, 2288, -824, -36433, 600283, -502708, 83638, -40071, 4098793, 1096584, -1160948, 3484553, -6256069, 4889852, -1520674, -276156781 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Define a shuffled sequence bb1(n) by taking the "original" Bernoulli numbers for even indices and the Bernoulli numbers for odd indices: bb1(2n) = A164555(n)/A027642(n), bb1(2n+1) = A027641(n)/A027642(n).

This starts bb1(n) = 1, 1, 1/2, -1/2, 1/6, 1/6, 0, 0, -1/30, -1/30, 0, 0, 1/42, 1/42,...

The inverse binomial transform of bb1(n) starts 1, 0, -1/2, 0, 13/6, -20/3, 14, -73/3 and its numerators define the current sequence.

LINKS

Table of n, a(n) for n=0..31.

MAPLE

bb1 := proc(n)

    nh := floor(n/2) ;

    if n <= 1 then

        bernoulli(nh) ;

    elif n <= 3 then

        -(-1)^n*bernoulli(nh) ;

    else

        bernoulli(nh) ;

    end if;

end proc:

[seq(bb1(n), n=0..40)] ;

read("transforms");

BINOMIALi(%) ;

numer(%) ; # R. J. Mathar, Mar 26 2013

CROSSREFS

Sequence in context: A145944 A330425 A335971 * A095040 A069195 A185126

Adjacent sequences:  A176147 A176148 A176149 * A176151 A176152 A176153

KEYWORD

frac,sign,uned

AUTHOR

Paul Curtz, Apr 10 2010, Apr 19 2010

STATUS

approved

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Last modified May 26 04:43 EDT 2022. Contains 354074 sequences. (Running on oeis4.)