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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read("transforms") ; L := [1,1/2,seq(bernoulli(2*i),i=1..30)] ; BINOMIALi(L) ; apply(denom,%) ;
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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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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
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
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