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A081901
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A sequence related to binomial(n+5, 5).
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2
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1, 8, 49, 262, 1286, 5944, 26262, 111996, 464103, 1877904, 7446735, 29021490, 111405780, 422003520, 1579757580, 5851519704, 21468622077, 78087814776, 281798184573, 1009617794334, 3593281988754, 12710491403112, 44705999907666
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OFFSET
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0,2
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COMMENTS
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Binomial transform of A055852.
2nd binomial transform of binomial(n+5, 5).
3rd binomial transform of (1,5,10,10,5,1,0,0,0,...).
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (18,-135,540,-1215,1458,-729).
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FORMULA
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a(n) = 3^n*(n^5 + 65*n^4 + 1385*n^3 + 11575*n^2 + 35574*n + 29160)/29160.
G.f.: (1 - 2*x)^5/(1 - 3*x)^6.
E.g.f.: (120 + 600*x + 600*x^2 + 200*x^3 + 25*x^4 + x^5)*exp(3*x)/120. - G. C. Greubel, Oct 18 2018
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MATHEMATICA
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LinearRecurrence[{18, -135, 540, -1215, 1458, -729}, {1, 8, 49, 262, 1286, 5944}, 50] (* G. C. Greubel, Oct 18 2018 *)
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PROG
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(PARI) x='x+O('x^30); Vec((1-2*x)^5/(1-3*x)^6) \\ G. C. Greubel, Oct 18 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-2*x)^5/(1-3*x)^6)); // G. C. Greubel, Oct 18 2018
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CROSSREFS
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Cf. A081902.
Sequence in context: A354558 A344321 A166789 * A283686 A026389 A005059
Adjacent sequences: A081898 A081899 A081900 * A081902 A081903 A081904
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KEYWORD
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nonn,easy
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AUTHOR
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Paul Barry, Mar 31 2003
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STATUS
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approved
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