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A037960
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a(n) = n*(3*n+1)*(n+2)!/24.
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8
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0, 1, 14, 150, 1560, 16800, 191520, 2328480, 30240000, 419126400, 6187104000, 97037740800, 1612798387200, 28332944640000, 524813313024000, 10226013557760000, 209144207720448000, 4480594531725312000, 100357207837286400000, 2345925761384325120000, 57136703662028390400000
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OFFSET
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0,3
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COMMENTS
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For n>=1, a(n) is equal to the number of surjections from {1,2,..,n+2} onto {1,2,...,n}. - Aleksandar M. Janjic and Milan Janjic, Feb 24 2007
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REFERENCES
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Identity (1.18) in H. W. Gould, Combinatorial Identities, Morgantown, 1972; page 3.
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LINKS
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FORMULA
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(3*n-2)*(n-1)*a(n) - n*(n+2)*(3*n+1)*a(n-1) = 0. - R. J. Mathar, Jul 26 2015
a(n) = n!*StirlingS2(n+2, n).
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MATHEMATICA
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Table[(n+2)!*n*(3n+1)/24, {n, 0, 20}] (* Harvey P. Dale, Oct 16 2014 *)
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PROG
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(Magma) [Factorial(n+2)*n*(3*n+1)/24: n in [0..25]]; // Vincenzo Librandi, Feb 20 2017
(SageMath) [factorial(n)*stirling_number2(n+2, n) for n in (0..30)] # G. C. Greubel, Jun 20 2022
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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