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A211611 Sum_{k=1..n-1} C(k)^n, where C(k) is a Catalan number. 3

%I

%S 1,9,642,540982,5496576970,698491214560174,1147342896257677900291,

%T 25005346993500437111980892595,7381619397278667883874693730628586499,

%U 30009934325456999669083059570156145437948880627,1703283943023520710008632777768663744247664926649672215939

%N Sum_{k=1..n-1} C(k)^n, where C(k) is a Catalan number.

%C The C(k) are the Catalan numbers, C(k) = A000108(k) = (2k)!/k!/(k+1)! = C(2*k,k)/(k+1).

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

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CatalanNumber.html">Catalan Number</a>

%F a(n) = Sum[ (Binomial[2 k, k]/(k + 1))^n, {k, 1, n - 1}].

%F a(n) ~ exp(3/8) * 4^(n^2-n) / (Pi^(n/2) * n^(3*n/2)). - _Vaclav Kotesovec_, Mar 03 2014

%t Table[ Sum[ (Binomial[2 k, k]/(k + 1))^n, {k, 1, n - 1}], {n, 2, 13}]

%Y Cf. A000108, A211610, A238717.

%K nonn

%O 2,2

%A _Alexander Adamchuk_, Apr 17 2012

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Last modified February 25 18:49 EST 2018. Contains 299655 sequences. (Running on oeis4.)