A308615 Denominators of the even shifted moments of the ternary Cantor measure.
1, 8, 320, 46592, 10915840, 128911704064, 3114038000353280, 798410297854394368, 35228168150276083007094784, 72984567358962659964369885986816, 2104733804502091904066890388853154119680, 146449616359318768962787815768964807513279037440
Offset: 0
Links
- Michael De Vlieger, Table of n, a(n) for n = 0..48
- Steven N. Harding, Alexander W. N. Riasanovsky, Moments of the weighted Cantor measures, arXiv:1908.05358 [math.FA], 2019.
Programs
-
Mathematica
f[0] = 1; f[n_] := f[n] = Sum[Binomial[n, j]*2^(n - j - 1)*f[j], {j, 0, n - 1}]/(3^n - 1); a[n_] := Sum[Binomial[n, j]*f[j]*(-1/2)^(n - j), {j, 0, n}]; Table[Denominator[a[i]], {i, 0, 24, 2}] (* Amiram Eldar, Aug 03 2019 *)
-
Sage
moms = [1] for k in [1..15]: s = 0 for j in [0..k-1]: s += binomial(k, j)*2^(k-j)*moms[j]/2 s /= (3^k-1) moms.append(s) x = var('x') shmoms = [] for k in [0..15]: p = (x-1/2)^k p = p.expand() s = 0 for m in [0..k]: s += moms[m]*p.coefficient(x, m) shmoms.append(s) [p.denominator() for p in shmoms[::2]]
Extensions
More terms from Amiram Eldar, Aug 03 2019
Comments