A365671 a(n) = denominator(4^n * n! * [x^n] sqrt(x / (e^x - 1))).

1, 1, 3, 1, 5, 3, 21, 3, 45, 5, 11, 1, 91, 35, 45, 3, 17, 3, 1995, 21, 3465, 165, 115, 45, 2925, 819, 189, 7, 145, 5, 341, 11, 1309, 119, 1, 1, 9139, 247, 65, 7, 2255, 495, 148995, 3465, 108675, 2415, 1645, 7, 270725, 5525, 21879, 429, 583, 33, 4389, 399, 4959

Offset: 0

Author

Peter Luschny, Sep 29 2023

Keywords

• nonn
• frac

Links

• Jitender Singh, On an arithmetic convolution, arXiv:1402.0065 [math.NT], 2014 and J. Int. Seq. 17 (2014) # 14.6.7.

Crossrefs

Cf. A241885 (numerator), A126156.

Programs

Maple

egf := sqrt(x/(exp(x)-1)): ser := series(egf, x, 64):
seq(denom(4^n*n!*coeff(ser,x,n)), n = 0..56);
# Alternative, using the Singh transformation 'g' from Maple in A126156:
b := n -> 4^n*g(bernoulli, n); seq(denom(b(n)), n = 0..56);