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A221953
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a(n) = 5^(n-1) * n! * Catalan(n-1).
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7
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1, 10, 300, 15000, 1050000, 94500000, 10395000000, 1351350000000, 202702500000000, 34459425000000000, 6547290750000000000, 1374931057500000000000, 316234143225000000000000, 79058535806250000000000000, 21345804667687500000000000000, 6190283353629375000000000000000, 1918987839625106250000000000000000
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OFFSET
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1,2
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COMMENTS
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a(n+1) is the number of square roots of any permutation in S_{20*n} whose disjoint cycle decomposition consists of 2*n cycles of length 10. - Luis Manuel Rivera Martínez, Feb 26 2015
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LINKS
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FORMULA
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a(1) = 1; a(n) = 5 * Sum_{k=1..n-1} binomial(n,k) * a(k) * a(n-k). - Ilya Gutkovskiy, Jul 10 2020
Sum_{n>=1} 1/a(n) = 1 + e^(1/20)*sqrt(Pi)*erf(1/(2*sqrt(5)))/(2*sqrt(5)), where erf is the error function.
Sum_{n>=1} (-1)^(n+1)/a(n) = 1 - e^(-1/20)*sqrt(Pi)*erfi(1/(2*sqrt(5)))/(2*sqrt(5)), where erfi is the imaginary error function. (End)
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MAPLE
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MATHEMATICA
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PROG
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(Magma) [Catalan(n-1)*5^(n-1)*Factorial(n): n in [1..20]]; // Vincenzo Librandi, Mar 11 2013
(PARI) my(x='x+O('x^22)); Vec(serlaplace((1-sqrt(1-20*x))/10)) \\ Michel Marcus, Mar 04 2015
(Sage) [5^(n-1)*factorial(n)*catalan_number(n-1) for n in (1..30)] # G. C. Greubel, Apr 02 2021
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CROSSREFS
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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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