A238717 -id:A238717 - cp's OEIS frontend

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

1, 9, 642, 540982, 5496576970, 698491214560174, 1147342896257677900291, 25005346993500437111980892595, 7381619397278667883874693730628586499, 30009934325456999669083059570156145437948880627, 1703283943023520710008632777768663744247664926649672215939

Offset: 2

Alexander Adamchuk, Apr 17 2012

nonn

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

p divides a(p) for prime p of the form p = 6k + 1 (A002476).

Eric Weisstein's World of Mathematics, Catalan Number

Cf. A000108, A002476, A211610, A238717.

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

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

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

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

Original entry on oeis.org

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

Offset: 2

Alexander Adamchuk, Apr 17 2012

nonn

2^n divides a(n).

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

Cf. A211611, A238717.

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

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

cp's OEIS Frontend

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

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