This site is supported by donations to The OEIS Foundation.

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 4500 articles have referenced us, often saying "we would not have discovered this result without the OEIS".

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A224783 Denominator of Bernoulli(n,1/2) - Bernoulli(n,0). 1
 1, 2, 4, 1, 16, 1, 64, 1, 256, 1, 1024, 1, 4096, 1, 16384, 1, 65536, 1, 262144, 1, 1048576, 1, 4194304, 1, 16777216, 1, 67108864, 1, 268435456, 1, 1073741824, 1, 4294967296, 1, 17179869184, 1, 68719476736, 1, 274877906944, 1, 1099511627776 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS See A157779 and A157780 for values of Bernoulli(n,1/2), and A027641 and A027642 for values of Bernoulli(n,0). B(n,1/2) - B(n,0) = 0, 1/2, -1/4, 0, 1/16, 0, -3/64, 0, 17/256, 0, -155/1024, 0, 2073/4096, 0, -38227/16384,... for n>=0. The sequence of numerators is 0, 1, -1, 0, 1, 0, -3, 0, 17, 0, -155, 0, 2073, 0, -38227, 0, 929569, 0, -28820619, 0, 1109652905,...and appears to contain a mix of A001469 and A036968. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..250 Index entries for linear recurrences with constant coefficients, signature (0,5,0,-4). FORMULA a(n) = A059222(n+1) if n <> 1. From Colin Barker, Mar 19 2014: (Start) G.f.: (4*x^5-9*x^3-x^2+2*x+1) / ((x-1)*(x+1)*(2*x-1)*(2*x+1)). a(n) = 5*a(n-2)-4*a(n-4) for n>5. a(n) = (1+(-2)^n-(-1)^n+2^n)/2 for n>1. (End). EXAMPLE a(0) = 1-1, a(1) = 0+1/2, a(2) = -1/12-1/6=-1/4. MAPLE A224783 := proc(n)     bernoulli(n, 1/2)-bernoulli(n) ;     denom(%) ; end proc: # R. J. Mathar, Apr 25 2013 MATHEMATICA Table[Denominator[BernoulliB[n, 1/2] - BernoulliB[n, 0]], {n, 0, 50}] (* Vincenzo Librandi, Mar 19 2014 *) PROG (PARI) Vec((4*x^5-9*x^3-x^2+2*x+1)/((x-1)*(x+1)*(2*x-1)*(2*x+1)) + O(x^100)) \\ Colin Barker, Mar 20 2014 CROSSREFS Cf. A001469, A027641, A027642, A036968, A059222, A157779, A157780. Sequence in context: A184176 A163546 A172385 * A214058 A173820 A030043 Adjacent sequences:  A224780 A224781 A224782 * A224784 A224785 A224786 KEYWORD nonn,frac,less,easy AUTHOR Paul Curtz, Apr 17 2013 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .