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A081900
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A sequence related to binomial(n+4, 4).
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2
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1, 9, 71, 519, 3606, 24150, 157250, 1001250, 6259375, 38534375, 234140625, 1406640625, 8367187500, 49335937500, 288632812500, 1676757812500, 9678955078125, 55548095703125, 317108154296875, 1801483154296875
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OFFSET
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0,2
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COMMENTS
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4th binomial transform of binomial(n+4, 4), A000332.
5th binomial transform of (1,4,6,4,1,0,0,0,...).
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LINKS
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FORMULA
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a(n) = 5^n*(n^4 + 74*n^3 + 1571*n^2 + 10354*n + 15000)/15000.
G.f.: (1 - 4*x)^4/(1 - 5*x)^5.
E.g.f.: (24 + 96*x + 72*x^2 + 16*x^3 + x^4)*exp(5*x)/24. - G. C. Greubel, Oct 18 2018
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MATHEMATICA
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LinearRecurrence[{25, -250, 1250, -3125, 3125}, {1, 9, 71, 519, 3606}, 50] (* G. C. Greubel, Oct 18 2018 *)
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PROG
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(PARI) x='x+O('x^30); Vec((1-4*x)^4/(1-5*x)^5) \\ G. C. Greubel, Oct 18 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-4*x)^4/(1-5*x)^5)); // G. C. Greubel, Oct 18 2018
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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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