A381268 a(n) = denominator( [(x*y*z*u)^n] 1/sqrt(1 - (x + y + z + u*(y + z))) ).
1, 4, 256, 1024, 1048576, 4194304, 268435456, 1073741824, 17592186044416, 70368744177664, 4503599627370496, 18014398509481984, 18446744073709551616, 73786976294838206464, 4722366482869645213696, 18889465931478580854784, 4951760157141521099596496896, 19807040628566084398385987584
Offset: 0
Links
- S. Hassani, J.-M. Maillard, and N. Zenine, On the diagonals of rational functions: the minimal number of variables (unabridged version), arXiv:2502.05543 [math-ph], 2025. See p. 24.
Programs
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Mathematica
a[n_]:=Denominator[SeriesCoefficient[1/Sqrt[1-(x+y+z+u(y+z))],{x,0,n},{y,0,n},{z,0,n},{u,0,n}]]; Array[a,13,0]
Formula
a(n) = denominator( [x^n] hypergeom( [1/2, 1/6, 1/2, 5/6], [1, 1, 1], 108*x) ).
a(n) = denominator( 2^(2*n-1) * 27^n * Gamma(n+1/6) * Gamma(n+1/2)^2 * Gamma(n+5/6)/(Pi^2 * (n!)^4) ).
a(2*n) = A278142(n).