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A037959
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a(n) = n^2*(n+1)*(n+2)!/48.
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2
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6, 90, 1200, 15750, 211680, 2963520, 43545600, 673596000, 10977120000, 188367379200, 3399953356800, 64457449056000, 1281520880640000, 26676557107200000, 580481882652672000, 13183287756807168000
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OFFSET
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2,1
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REFERENCES
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Identity (1.19)/(n+3) in H. W. Gould, Combinatorial Identities, Morgantown, 1972, page 3.
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LINKS
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FORMULA
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(n-1)^2*a(n) = n*(n+2)*(n+1)*a(n-1). - R. J. Mathar, Jul 26 2015
a(n) = (1/(n+3))*Sum_{j=0..n} (-1)^(n+j)*binomial(n,j)*j^(n+3).
a(n) = n!*StirlingS2(n+3, n)/(n+3).
E.g.f.: x*(1 + 6*x + 3*x^2)/(4*(1-x)^6). (End)
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MATHEMATICA
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Table[(n+2)!n^2(n+1)/48, {n, 2, 20}] (* Harvey P. Dale, Jul 29 2021 *)
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PROG
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(Magma) [Factorial(n)*StirlingSecond(n+3, n)/(n+3): n in [2..30]]; // G. C. Greubel, Jun 20 2022
(SageMath) [factorial(n)*stirling_number2(n+3, n)/(n+3) for n in (2..30)] # G. C. Greubel, Jun 20 2022
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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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