A381161 a(n) = (10*n)!/((n!)^3*(2*n)!*(5*n)!).

1, 15120, 3491888400, 1304290155168000, 601680868708529610000, 312696069714024464473125120, 175460887238127057573116837126400, 103865765423748548466734695459219968000, 63958974275578307119821712720619705931210000, 40596987692554701292235753375257230410967703200000

Offset: 0

Author

Stefano Spezia, Feb 15 2025

Keywords

• nonn

Comments

Calabi-Yau series number 2.

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 p. 14.

Crossrefs

Cf. A000442, A010050, A100734, A195394.

Cf. A381162, A381163, A381164, A381165.

Programs

Mathematica

a[n_]:=(10n)!/((n!)^3*(2n)!*(5n)!); Array[a,10,0]

Formula

G.f.: hypergeom([1/10, 3/10, 7/10, 9/10], [1, 1, 1], 2^8*5^5*x).

a(n) ~ 9*2^(3+8*n)*5^(1+5*n)/((1 + 24*n)*(1 + 60*n)*Pi^2).