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A081895
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Second binomial transform of binomial(n+3, 3).
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3
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1, 6, 30, 136, 579, 2358, 9288, 35640, 133893, 494262, 1797714, 6456024, 22930695, 80660934, 281309436, 973599912, 3346483977, 11431295910, 38828142342, 131206405608, 441271936971, 1477621745046, 4927988620080, 16373939547096
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OFFSET
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0,2
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COMMENTS
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2nd binomial transform of binomial(n+3, 3), A000292.
3rd binomial transform of (1,3,3,1,0,0,0,0,...).
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LINKS
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FORMULA
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a(n) = 3^n*(n^3 + 24*n^2 + 137*n + 162)/162.
G.f.: (1 - 2*x)^3/(1 - 3*x)^4.
E.g.f.: (6 + 18*x + 9*x^2 + x^3)*exp(3*x)/6. - G. C. Greubel, Oct 18 2018
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MATHEMATICA
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LinearRecurrence[{12, -54, 108, -81}, {1, 6, 30, 136}, 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)^3/(1-3*x)^4) \\ G. C. Greubel, Oct 18 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-2*x)^3/(1-3*x)^4)); // 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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