A211610 a(n) = Sum_{k=1..n-1} binomial (2*k, k)^n.

4, 224, 161312, 1683907808, 256213978094784, 575112148876911852416, 19248204431728945392010740480, 9687459136669902998216039379883774976, 73815961078227084527800998811241905249902260224, 8562177846610881578580018959490439733543225146878872883200

Offset: 2

Author

Alexander Adamchuk, Apr 17 2012

Keywords

• nonn

Comments

2^n divides a(n).

p divides a(p) for prime p of the form p = 6k + 1.

Crossrefs

Cf. A211611, A238717.

Programs

Mathematica

Table[ Sum[ Binomial[2 k, k]^n, {k, 1, n - 1}], {n, 2, 13}]

Formula

a(n) = Sum_{k=1..n-1} binomial(2*k, k)^n.

a(n) ~ exp(3/8) * 4^(n^2-n) / (Pi^(n/2) * n^(n/2)). - Vaclav Kotesovec, Mar 03 2014