A381296 - OEIS

%I #7 Feb 20 2025 08:37:40

%S 1,1,16,1,4096,4096,16384,8192,268435456,268435456,4294967296,

%T 1073741824,274877906944,274877906944,2199023255552,1099511627776,

%U 1152921504606846976,1152921504606846976,18446744073709551616,2305843009213693952,4722366482869645213696,4722366482869645213696

%N a(n) = denominator( [(x*y*z*u*v)^n] 1/sqrt(1 - (x + y + z + u + v*(x*y*z + x*y*u + x*z*u + y*z*u))) ).

%H S. Hassani, J.-M. Maillard, and N. Zenine, <a href="https://arxiv.org/abs/2502.05543">On the diagonals of rational functions: the minimal number of variables (unabridged version)</a>, arXiv:2502.05543 [math-ph], 2025. See p. 44.

%t a[n_]:=Denominator[SeriesCoefficient[1/Sqrt[1-(x+y+z+u+v(x*y*z+x*y*u+x*z*u+y*z*u))],{x,0,n},{y,0,n},{z,0,n},{u,0,n},{v,0,n}]]; Array[a,22,0]

%Y Cf. A381295 (numerator).

%K nonn,frac,new

%O 0,3

%A _Stefano Spezia_, Feb 19 2025