cp's OEIS Frontend

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.

Showing 1-3 of 3 results.

A174276 Denominator of the n-th term of the inverse binomial transform of 1, 1/2, B_4, B_6, B_8,..., a modified Bernoulli sequence.

Original entry on oeis.org

1, 2, 6, 30, 70, 210, 2310, 10010, 6006, 510510, 461890, 9699690, 31870410, 74364290, 223092870, 6469693230, 6077590610, 200560490130, 200560490130, 494715875654, 674612557710, 60850052705442, 872184088778002, 13082761331670030
Offset: 0

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Author

Paul Curtz, Mar 14 2010

Keywords

Comments

The numerators are in A174289. The input sequence starts 1, 1/2, 1/6, -1/30, 1/42....
The inverse binomial transform generates 1, -1/2, 1/6, -1/30, 11/70, -137/210, 4157/2310,...

Crossrefs

Programs

  • Maple
    read("transforms") ; L := [1,1/2,seq(bernoulli(2*i),i=1..30)] ; BINOMIALi(L) ; apply(denom,%) ;
  • Mathematica
    b[0]=1; b[1]=1/2; b[n_] := BernoulliB[2n-2]; a[n_] := Sum[(-1)^(n-k)*Binomial[n, k]*b[k], {k, 0, n}]; Table[a[n], {n, 0, 23}] // Denominator (* Jean-François Alcover_, Aug 09 2012 *)

A174290 Numerators of the inverse binomial transform of the sequence of nonzero Bernoulli numbers.

Original entry on oeis.org

1, -3, 13, -91, 291, -1187, 18017, -114949, 122399, -27857449, 118047751, -18228890369, 594111334397, -17200311140979, 773613644762857, -398027494487496919, 7730820144185428909, -6072430940814524211839
Offset: 0

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Author

Paul Curtz, Mar 15 2010

Keywords

Comments

The sequence of nonzero Bernoulli numbers is B(0), B(1), B(2), B(4), B(6) etc. Its inverse Bernoulli transform is 1, -3/2, 13/6, -91/30, 291/70, -1187/210, 18017/2310,... The current sequence is defined by extracting the numerators.

Crossrefs

Cf. A174276 (denominators), A174289.

Programs

  • Maple
    read("transforms") ;
    A174290 := proc(n) [1, -1/2, seq(bernoulli(2*i), i=1..30)] ; BINOMIALi(%) ; numer(op(n+1,%)) ; end proc:
    seq(A174290(n),n=0..30) ; # R. J. Mathar, Jan 21 2011

A174356 (-1)^(n+1)*n*A174276(n).

Original entry on oeis.org

0, 2, -12, 90, -280, 1050, -13860, 70070, -48048, 4594590, -4618900, 106696590, -382444920, 966735770, -3123300180, 97045398450, -97241449760, 3409528332210, -3610088822340, 9399601637426, -13492251154200
Offset: 0

Views

Author

Paul Curtz, Mar 17 2010

Keywords

Comments

The sequence obeys a(n) = A174289(n) - A174290(n), a formula that might be compared to A164869(n) = n*A027642(n) = A164558(n)-A164555(n).
Showing 1-3 of 3 results.