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A211611
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Sum_{k=1..n-1} C(k)^n, where C(k) is a Catalan number.
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3
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1, 9, 642, 540982, 5496576970, 698491214560174, 1147342896257677900291, 25005346993500437111980892595, 7381619397278667883874693730628586499, 30009934325456999669083059570156145437948880627, 1703283943023520710008632777768663744247664926649672215939
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OFFSET
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2,2
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COMMENTS
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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.
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LINKS
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Table of n, a(n) for n=2..12.
Eric Weisstein's World of Mathematics, Catalan Number
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FORMULA
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a(n) = Sum[ (Binomial[2 k, k]/(k + 1))^n, {k, 1, n - 1}].
a(n) ~ exp(3/8) * 4^(n^2-n) / (Pi^(n/2) * n^(3*n/2)). - Vaclav Kotesovec, Mar 03 2014
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MATHEMATICA
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Table[ Sum[ (Binomial[2 k, k]/(k + 1))^n, {k, 1, n - 1}], {n, 2, 13}]
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CROSSREFS
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Cf. A000108, A211610, A238717.
Sequence in context: A158881 A188394 A157597 * A210053 A128795 A191510
Adjacent sequences: A211608 A211609 A211610 * A211612 A211613 A211614
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KEYWORD
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nonn
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AUTHOR
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Alexander Adamchuk, Apr 17 2012
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STATUS
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approved
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