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A107251
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Supercatalan numbers SF(2n)/(SF(n)*SF(n+1)) where SF is the superfactorial function A000178.
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1
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1, 1, 12, 7200, 508032000, 7742895390720000, 40797452088662556672000000, 108985983996792124183843071590400000000, 203800994173724454677862841368011757060096000000000000
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) ~ A * 2^(2*n^2 + 2*n - 7/12) * n^(n^2 - n - 23/12) / (Pi * exp(3*n^2/2 - n + 1/12)), where A = A074962 = 1.2824271291... is the Glaisher-Kinkelin constant. - Vaclav Kotesovec, Jul 10 2015
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EXAMPLE
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a(3) = 1!*2!*3!*4!*5!*6!/(1!*2!*3!*1!*2!*3!*4!) = 24883200/(12*288) = 7200.
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MAPLE
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CROSSREFS
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Cf. A000108 for original Catalan numbers (2n)!/(n!*(n+1)!).
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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