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A091545
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First column sequence of the array (7,2)-Stirling2 A091747.
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1
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1, 42, 5544, 1507968, 696681216, 489070213632, 485157651922944, 646229992361361408, 1112808046846264344576, 2405890997281623512973312, 6380422924790865556405223424, 20366309975932442856045473169408
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OFFSET
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1,2
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COMMENTS
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Also sixth column (m=5) sequence of triangle A091543.
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REFERENCES
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P. Blasiak, K. A. Penson and A. I. Solomon, The general boson normal ordering problem, Phys. Lett. A 309 (2003) 198-205.
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LINKS
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FORMULA
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a(n)= product((5*j+2)*(5*j+1), j=0..n-1)/2, n>=1. From eq.12 of the Blasiak et al. reference with r=7, s=2, k=1.
a(n)= (5^(2*n))*risefac(1/5, n)*risefac(2/5, n)/2, n>=1, with risefac(x, n) = Pochhammer(x, n).
a(n)= fac5(5*n-3)*fac5(5*n-4)/2, n>=1, with fac5(5*n-4)/2 = A034323(n) and fac5(5*n-3)= A008548(n) (5-factorials).
E.g.f.: (hypergeom([1/5, 2/5], [], 25*x)-1)/2.
D-finite with recurrence a(n) -(5*n-3)*(5*n-4)*a(n-1)=0. - R. J. Mathar, Jul 27 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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STATUS
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approved
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