A381292 Expansion of g.f. hypergeom([1/2, 3/4, 5/4], [1, 3/2], 256*x).

1, 80, 12096, 2196480, 435635200, 91017658368, 19681596211200, 4361120388218880, 984138122900275200, 225245492144504832000, 52138539404512009912320, 12180522019129546663526400, 2867511425916768698757021696, 679455041354637369514813030400, 161892954188496214335204360192000

Offset

0,2

Links

Table of n, a(n) for n=0..14.

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. 42.

Formula

a(n) = 2^(6*n+1)*Gamma(2*n+3/2)/((2*n+1)*sqrt(Pi)*(n!)^2).

Mathematica

a[n_]:=2^(6n+1)Gamma[2n+3/2]/((2n+1)Sqrt[Pi]n!^2); Array[a, 15, 0]

Crossrefs

Cf. A001044, A277757.

Sequence in context: A091754 A118493 A265846 * A269145 A187052 A159377

Adjacent sequences: A381289 A381290 A381291 * A381295 A381296 A381297

Keyword

nonn,new

Author

Stefano Spezia, Feb 19 2025

Status

approved