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A081899
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A sequence related to binomial(n+4, 4).
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3
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1, 8, 54, 332, 1921, 10644, 57072, 298176, 1525248, 7665664, 37953536, 185499648, 896466944, 4289462272, 20343422976, 95718211584, 447146360832, 2075274510336, 9574555844608, 43933220470784, 200579267690496
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OFFSET
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0,2
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COMMENTS
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3rd binomial transform of binomial(n+4, 4), A000332.
4th 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) = 4^n*(n^4 + 58*n^3 + 971*n^2 + 5114*n + 6144)/6144.
G.f.: (1 - 3*x)^4/(1 - 4*x)^5.
E.g.f.: (24 + 96*x + 72*x^2 + 16*x^3 + x^4)*exp(4*x)/24. - G. C. Greubel, Oct 18 2018
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MATHEMATICA
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LinearRecurrence[{20, -160, 640, -1280, 1024}, {1, 8, 54, 332, 1921}, 50] (* G. C. Greubel, Oct 18 2018 *)
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PROG
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(PARI) x='x+O('x^30); Vec((1-3*x)^4/(1-4*x)^5) \\ G. C. Greubel, Oct 18 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-3*x)^4/(1-4*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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