A381162 a(n) = (8*n)!/((n!)^4*(4*n)!).

1, 1680, 32432400, 999456057600, 37905932634570000, 1617318175088527591680, 74451445170005824874553600, 3614146643656788883257309696000, 182458061523203642337177421198794000, 9493111901274733909567003010522405280000, 505860213332178847817809654781948251947782400

Offset: 0

Author

Stefano Spezia, Feb 15 2025

Keywords

• nonn

Comments

Calabi-Yau series number 7.

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 pp. 14-15.

Crossrefs

Cf. A100733, A134375, A195392.

Cf. A381161, A381163, A381164, A381165.

Programs

Mathematica

a[n_]:=(8n)!/((n!)^4*(4n)!); Array[a,11,0]

Formula

G.f.: hypergeom([1/8, 3/8, 5/8, 7/8], [1, 1, 1], 2^16*x).

a(n) ~ 2^(16*n - 3/2) / (Pi^2*n^2). - Vaclav Kotesovec, May 29 2025