A341476 Coefficients related to the asymptotics of generalized Delannoy numbers.

1, 3, 22, 223, 2792, 42671, 761984, 15707707, 365122688, 9491746747, 271962399232, 8539383210711, 290937486190592, 10710312199270503, 422984587596455936, 17864076455770831219, 802450164859200372736, 38242916911507537149427, 1925477163696152909447168, 102213291475268656299164879

Offset: 1

Author

Vaclav Kotesovec, Feb 13 2021

Keywords

• nonn

Examples

			Lim_{n->infinity} A001850(n)^(1/n) = (    3 +    2 * sqrt(1^2 + 1)) / 1^1.
Lim_{n->infinity} A026000(n)^(1/n) = (   22 +   10 * sqrt(2^2 + 1)) / 2^2.
Lim_{n->infinity} A026001(n)^(1/n) = (  223 +   70 * sqrt(3^2 + 1)) / 3^3.
Lim_{n->infinity} A331329(n)^(1/n) = ( 2792 +  680 * sqrt(4^2 + 1)) / 4^4.
Lim_{n->infinity} A341491(n)^(1/n) = (42671 + 8346 * sqrt(5^2 + 1)) / 5^5.
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A008288, A001850, A026000, A026001, A331329, A341491, A341477.

Formula

Lim_{n->infinity} (binomial(k*n, n) * hypergeom([(1-k)*n, -n], [-k*n], -1))^(1/n) = (A341476(k) + A341477(k)*sqrt((k-1)^2 + 1)) / (k-1)^(k-1), for k>1.

Lim_{n->infinity} hypergeom([(1-k)*n, -n], [-k*n], -1)^(1/n) = (A341476(k) + A341477(k)*sqrt((k-1)^2 + 1)) / k^k.

For k > 1, A341476(k)^2 - ((k-1)^2 + 1) * A341477(k)^2 = (-1)^k * (k-1)^(2*k-2).

Lim_{k->infinity} (A341476(k) + A341477(k)*sqrt((k-1)^2 + 1)) / (k * (k-1)^(k-1)) = 2*exp(1).

a(n) ~ n^n.