A341491 a(n) = binomial(6*n, n) * hypergeom([-5*n, -n], [-6*n], -1).

1, 11, 221, 4991, 118721, 2908411, 72616013, 1837271615, 46943003137, 1208483403179, 31297149356221, 814471993937855, 21281058718583873, 557930580979801755, 14669716953106628781, 386675596518995000191, 10214494658006725840897, 270345191656309313382475

Offset: 0

Author

Vaclav Kotesovec, Feb 13 2021

Keywords

• nonn

Comments

In general, for k > 1, binomial(k*n, n) * hypergeom([(1-k)*n, -n], [-k*n], -1) ~ sqrt((k + (k^2 - k + 1) / sqrt(k^2 - 2*k + 2)) / (4*(k-1)*Pi*n)) * ((A341476(k) + A341477(k)*sqrt((k-1)^2 + 1)) / (k-1)^(k-1))^n.

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..697
• Lin Yang, Yu-Yuan Zhang, and Sheng-Liang Yang, The halves of Delannoy matrix and Chung-Feller properties of the m-Schröder paths, Linear Alg. Appl. (2024).

Crossrefs

Cf. A001850, A026000, A026001, A331329, A341476, A341477.

Programs

Mathematica

Table[Binomial[6*n, n] * Hypergeometric2F1[-5*n, -n, -6*n, -1], {n,0,20}]

Formula

a(n) ~ sqrt((6 + 31/sqrt(26))/(20*Pi*n)) * (42671 + 8346*sqrt(26))^n / 5^(5*n).