A081899 Third binomial transform of binomial(n+4, 4).
1, 8, 54, 332, 1921, 10644, 57072, 298176, 1525248, 7665664, 37953536, 185499648, 896466944, 4289462272, 20343422976, 95718211584, 447146360832, 2075274510336, 9574555844608, 43933220470784, 200579267690496, 911512319295488, 4124474274217984, 18588068701274112
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (20,-160,640,-1280,1024).
Programs
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Magma
m:=30; R
:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-3*x)^4/(1-4*x)^5)); // G. C. Greubel, Oct 18 2018 -
Mathematica
LinearRecurrence[{20,-160,640,-1280,1024}, {1,8,54,332,1921}, 50] (* G. C. Greubel, Oct 18 2018 *) -
PARI
x='x+O('x^30); Vec((1-3*x)^4/(1-4*x)^5) \\ G. C. Greubel, Oct 18 2018
Formula
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
Comments