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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 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.)