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

0,2

Links

Table of n, a(n) for n=0..17.

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.

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).

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]

Crossrefs

Cf. A381267 (numerator).

Cf. A009971, A134375, A278142.

Sequence in context: A203511 A063073 A377383 * A093760 A062075 A266890

Adjacent sequences: A381265 A381266 A381267 * A381269 A381270 A381271

Keyword

nonn,frac

Author

Stefano Spezia, Feb 18 2025

Status

approved