A181722
Numerator of (1/n - Bernoulli number A164555(n)/A027642(n)).
Original entry on oeis.org
0, 0, 1, 1, 7, 1, 5, 1, 13, 1, 1, 1, 901, 1, -11, 1, 3647, 1, -43825, 1, 1222387, 1, -854507, 1, 1181821001, 1, -76977925, 1, 23749461059, 1, -8615841275543, 1, 28267510484519, 1
Offset: 1
Fractions are 0, 0, 1/6, 1/4, 7/30, 1/6, 5/42, 1/8, 13/90, 1/10, 1/66, 1/12, 901/2730, ...
-
A181722:= func< n | n le 2 select 0 else Numerator(1/n - Bernoulli(n-1)) >;
[A181722(n): n in [1..40]]; // G. C. Greubel, Mar 25 2024
-
a[n_] := If[n <= 2, 0, Numerator[1/n - BernoulliB[n-1]]];
Table[a[n], {n, 1, 34}] (* Jean-François Alcover, Jun 07 2017 *)
-
def A181722(n): return 0 if n<3 else numerator(1/n - bernoulli(n-1))
[A181722(n) for n in range(1,41)] # G. C. Greubel, Mar 25 2024
A174111
Denominators of the image of a modified Bernoulli-number sequence under the Akiyama-Tanigawa transform.
Original entry on oeis.org
2, 3, 2, 15, 6, 7, 6, 15, 10, 33, 6, 455, 210, 3, 2, 255, 30, 133, 42, 33, 110, 69, 6, 455, 546, 3, 2, 435, 30, 2387, 462
Offset: 0
-
read("transforms3") ;
A174111 := proc(n) Lin := [bernoulli(0),-bernoulli(1),seq(bernoulli(k),k=2..n+1)] ; AKIYATANI(Lin) ; denom(op(n+1,%)) ; end proc:
-
b[0]=0; b[1]=1; b[2]=1/2; b[n_] := BernoulliB[n-1]; a[0, m_] := b[m+1]; a[n_, m_] := a[n, m] = (m+1)*(a[n-1, m] - a[n-1, m+1]); Table[a[1, m], {m, 0, 30}] // Denominator (* Jean-François Alcover, Aug 09 2012 *)
A174129
Numerators of the first column of the table of fractions generated by the Akiyama-Tanigawa transform from a first row A164555(k)/A027642(k).
Original entry on oeis.org
1, 1, -1, -1, 31, 7, -1051, -201, 56911, 18311, -24346415, -4227881, 425739604981, 2082738855, -759610463437, -1935668684041, 91825384886337407, 3104887811293639, -333936446105326262497, -8039608511660213481, 496858217433153341005061
Offset: 0
-
read("transforms3") ;
A174129 := proc(n) Lin := [bernoulli(0),-bernoulli(1),seq(bernoulli(k),k=2..n+1)] ; for r from 1 to n do Lin := AKIYATANI(Lin) ; end do; numer(op(1,Lin)) ; end proc:
-
a[0, k_] := a[0, k] = BernoulliB[k]; a[0, 1] = 1/2; a[n_, k_] := a[n, k] = (k+1)*(a[n-1, k] - a[n-1, k+1]); a[n_] := a[n, 0] // Numerator; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Aug 14 2012 *)
Showing 1-3 of 3 results.
Comments