A285865 Denominator of the coefficient triangle B2(n, m) of generalized Bernoulli polynomials PB2(n, x) read by rows.
1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 15, 1, 1, 1, 1, 1, 3, 1, 3, 1, 1, 21, 1, 1, 1, 1, 1, 1, 1, 3, 1, 3, 1, 1, 1, 1, 15, 1, 3, 1, 3, 1, 3, 1, 1, 1, 5, 1, 1, 1, 5, 1, 1, 1, 1, 33, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
Offset: 0
Examples
The triangle a(n, m) begins: n\m 0 1 2 3 4 5 6 7 8 9 10 ... 0: 1 1: 1 1 2: 3 1 1 3: 1 1 1 1 4: 15 1 1 1 1 5: 1 3 1 3 1 1 6: 21 1 1 1 1 1 1 7: 1 3 1 3 1 1 1 1 8: 15 1 3 1 3 1 3 1 1 9: 1 5 1 1 1 5 1 1 1 1 10: 33 1 1 1 1 1 1 1 1 1 1 ... For the triangle of the rationals B2(n, m) see A285864.
Programs
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Mathematica
T[n_, m_]:=Denominator[Binomial[n, m]*2^(n - m)*BernoulliB[n - m]]; Table[T[n, m], {n, 0, 20}, {m, 0, n}] // Flatten (* Indranil Ghosh, May 06 2017 *) -
PARI
T(n, m) = denominator(binomial(n, m)*2^(n - m)*bernfrac(n - m)); for(n=0, 20, for(m=0, n, print1(T(n, m),", ");); print();) \\ Indranil Ghosh, May 06 2017
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Python
from sympy import binomial, bernoulli def T(n, m): return (binomial(n, m) * 2**(n - m) * bernoulli(n - m)).denominator for n in range(21): print([T(n, m) for m in range(n + 1)]) # Indranil Ghosh, May 06 2017
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