A381297 a(n) = numerator( [x^n] hypergeom([1/2, 1/2, 1/2, 1/4, 3/4], [1, 1, 1, 1], 256*x) ).

1, 6, 2835, 144375, 9656521875, 727613515629, 1924950961452519, 169849119537100575, 515343459815505282121875, 49523686986654845229890625, 156852007784587147805477109405, 15901454576103641443903862431665, 1683931647757461343713885153275036775, 177089976268148398718338641838887890625

Offset

0,2

Links

Table of n, a(n) for n=0..13.

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. 46.

Formula

a(n) = numerator( 4*(4*n - 1)!*Gamma(n+1/2)^2/(Pi*(n-1)!*(n!)^5) ) with a(0) = 1.

Mathematica

a[0]=1; a[n_]:=Numerator[4*(4*n - 1)!*Gamma[n+1/2]^2/(Pi*(n-1)!n!^5)]; Array[a, 14, 0]

Crossrefs

Cf. A381298 (denominator).

Sequence in context: A097871 A210004 A198667 * A225066 A001326 A300851

Adjacent sequences: A381294 A381295 A381296 * A381298 A381299 A381300

Keyword

nonn,frac

Author

Stefano Spezia, Feb 19 2025

Status

approved