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
A174289
Numerator 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, -1, 1, -1, 11, -137, 4157, -44879, 74351, -23262859, 113428851, -18122193779, 593728889477, -17199344405209, 773610521462677, -398027397442098469, 7730820046943979149, -6072430937404995879629, 164713122370768078443379
Offset: 0
-
read("transforms") ;
L := [1,1/2,seq(bernoulli(2*i),i=1..30)] ;BINOMIALi(L) ; apply(numer,%) ; # R. J. Mathar, Dec 02 2010
-
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, 18}] // Numerator (* 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
-
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
A176546
Bernoulli numerators A000367 with an additional 1 inserted to represent B_1.
Original entry on oeis.org
1, 1, 1, -1, 1, -1, 5, -691, 7, -3617, 43867, -174611, 854513, -236364091, 8553103, -23749461029, 8615841276005, -7709321041217, 2577687858367, -26315271553053477373, 2929993913841559, -261082718496449122051
Offset: 0
B_0=1/1, B_1=1/2 "originally", B_2=1/6, B_4=-1/30, B_6=1/42,...
Showing 1-4 of 4 results.
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