A132096
Numerators of Blandin-Diaz compositional Bernoulli numbers (B^Z)_1,n.
Original entry on oeis.org
1, -1, 1, 1, 61, -1, -12491, -479, 530629, 54979, 1039405, -4981183, -9055875786121, 908993573959, 288260975797477, 7874837285353, -2255621632465386299, -189404901989770501, -20038592583515962234111, 954329155426992424481, 1731149375200514221429374109
Offset: 0
1, -1/4, 1/72, 1/96, 61/21600, -1/640, -12491/5080320, -479/680608.
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nn = 21; A = Inverse[Table[Table[If[n >= k, Binomial[n - 1, k - 1]/(n - k + 1)^2, 0], {k, 1, nn}], {n, 1, nn}]]; Numerator[A[[All, 1]]] (* Mats Granvik, Feb 05 2018 *)
A133000
Numerators of Blandin-Diaz compositional Bernoulli numbers (B^Z^(3))_1,n.
Original entry on oeis.org
60, -15, 9, 3, 401, 127, -9089, -192233
Offset: 0
60, -15/12, 9/56, 3/64, 401/31360, 127/50176, -9089/33116160, -192233/264929280.
A133001
Denominators of Blandin-Diaz compositional Bernoulli numbers (B^Z^(3))_1,n.
Original entry on oeis.org
1, 12, 56, 64, 31360, 50176, 33116160, 264929280
Offset: 0
60, -15/12, 9/56, 3/64, 401/31360, 127/50176, -9089/33116160, -192233/264929280.
A133004
Numerators of Blandin-Diaz compositional Bernoulli numbers C_2,n.
Original entry on oeis.org
0, 1, -2, 5, -68, 193, -655, 19349, -57736, 520343, -43184789, 366043159, -36085302154, 219183008719, -333043820161, 1124780733391, -2033896175720464, 6178608669563333, -106918567902798017, 178383998798531120359, -54061775649488096702, 2291400664110090118501, -56920102349900658177643
Offset: 0
0, 1, -23, 56, -68/45, 193/54, -655/63, 19349/540, -57736/405, 520343/810.
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my(x='x+O('x^30)); apply(numerator, concat(0, Vec(serlaplace(serreverse(2*(exp(x)-1-x)/x))))) \\ Michel Marcus, Jan 24 2024
A133005
Denominators of Blandin-Diaz compositional Bernoulli numbers C_2,n.
Original entry on oeis.org
1, 1, 3, 6, 45, 54, 63, 540, 405, 810, 13365, 20412, 331695, 306180, 65610, 29160, 6506325, 2296350, 4363065, 757795500, 22733865, 90935460, 203719050, 9672226200, 403009425, 4836113100, 22320522, 2232052200, 267009244425, 6313519080, 3425084100900, 112696315578000, 3018651310125
Offset: 0
0, 1, -23, 56, -68/45, 193/54, -655/63, 19349/540, -57736/405, 520343/810.
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my(x='x+O('x^40)); apply(denominator, concat(0, Vec(serlaplace(serreverse(2*(exp(x)-1-x)/x))))) \\ Michel Marcus, Jan 24 2024
A133002
Numerators of Blandin-Diaz compositional Bernoulli numbers (B^S)_1,n.
Original entry on oeis.org
1, -1, 5, -1, 139, -1, 859, 71, -9769, 233, -6395527, 145069, -304991568097, -95164619917, 119780081383, -3046785293, 4002469707564917, -102407337854027, 1286572077762833639, 219276930957009857, -20109624681057406222913, 1651690537394493957719
Offset: 0
1, -1/4, 5/72, -1/48, 139/21600, -1/540, 859/2540160, 71/483840, -9769/36288000 (corrected by _Daniel Suteu_, Feb 24 2018).
Corrected the sign of a(0) and a(3) by
Daniel Suteu, Feb 24 2018
A133003
Denominators of Blandin-Diaz compositional Bernoulli numbers (B^S)_1,n.
Original entry on oeis.org
1, 4, 72, 48, 21600, 540, 2540160, 483840, 36288000, 896000, 31614105600, 1149603840, 7139902049280000, 2196892938240000, 941525544960000, 15216574464000, 16326052949606400000, 443241256550400000, 11991344662654156800000, 1100420292929126400000
Offset: 0
1, -1/4, 5/72, -1/48, 139/21600, -1/540, 859/2540160, 71/483840, -9769/36288000 (corrected by _Daniel Suteu_, Feb 24 2018).
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f[0] = 1; f[n_] := f[n] = -Sum[f[k]/((n - k + 1)!)^2, {k, 0, n - 1}]; a[n_] := Denominator[f[n]*n!]; Table[a[n], {n, 0, 19}] (* Jean-François Alcover, Feb 25 2018, after Daniel Suteu *)
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