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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A233565 Numerators of the autosequence preceding Br(n)=A229979(n)/(1 followed by A050932(n)).

Original entry on oeis.org

0, 0, 0, 1, 2, 5, 5, 7, 7, 5, 5, 11, 11, 91, 91, -9, -9, 1207, 1207, -10849, -10849, 65879, 65879, -783127, -783127, 61098739, 61098739, -2034290233, -2034290233, 72986324461, 72986324461
Offset: 0

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Author

Paul Curtz, Dec 13 2013

Keywords

Comments

Br(n)=0, 1, 1, 1/2, 0, -1/6, 0, 1/6, 0, -3/10, 0, 5/6, 0, -691/210, 0,.. .
a(n) is the numerators of Bp2(n)=0, 0, 0, 1, 2, 5/2, 5/2, 7/3, 7/3, 5/2, 5/2, 11/5, 11/5, 91/30, 91/30,... . Bp2(n) is an autosequence like Br(n).
With possible future sequences we can write the array PB
1, 0, 0, 0, 0, 0, 0, 0, 0,
1, 1, 0, 0, 0, 0, 0, 0, 0,
1, 3/2, 1, 0, 0, 0, 0, 0, 0,
1, 5/3, 2, 1, 0, 0, 0, 0, 0,
1, 5/3, 5/2, 5/2, 1, 0, 0, 0, 0,
1, 49/30, 5/2, 7/2, 3, 1, 0, 0, 0,
1, 49/30, 7/3, 7/2, 14/3, 7/2, 1, 0, 0,
1, 58/35, 7/3, 3, 14/3, 6, 4, 1, 0,
1, 58/35, 5/2, 3, 7/2, 6, 15/2, 9/2, 1, etc.
The first column is A000012. The second A165142(n+1)/(1 followed by A100650(n)). The third is Bp2(n+1). The next others are built by the same way. From the second,every column is based on A164555(n)/A027642(n).
With negative (2*n+2)-th diagonals,the array without 0's is the triangle NPB. The sum of every row is
1, 0, 1/2, -1/3, 1/3, -11/30, 11/30, -12/35, 12/35, -79/210, 79/210,... .
See A176250(n+2)/A100650(n).
The inverse of NPB is A193815(n)/(A003056(n) with 1 instead of 0).

Examples

			a(0)=a(1)=0, a(i)=numerators of 0+Br(0)=0, 0+Br(1)=1, 1+Br(2)=2, 2+Br(3)=5/2, 5/2+Br(4)=5/2,... .

Crossrefs

Cf. A233316.

Programs

  • Mathematica
    nmax = 30; Br[0] = 0; Br[1] = Br[2] = 1; Br[n_] := Numerator[2*n*BernoulliB[n-1]] / Denominator[n*BernoulliB[n-1]]; Bp2 = Join[{0, 0}, Table[Br[n], {n, 0, nmax-2}] // Accumulate]; a[n_] := Numerator[Bp2[[n+1]]]; Table[a[n], {n, 0, nmax}] (* Jean-François Alcover, Dec 18 2013 *)

Extensions

a(17)-a(30) from Jean-François Alcover, Dec 18 2013
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