A081907 Fifth binomial transform of binomial(n+2, 2).
1, 8, 61, 450, 3240, 22896, 159408, 1096416, 7464960, 50388480, 337602816, 2247326208, 14874679296, 97955205120, 642150789120, 4192482779136, 27270729105408, 176789554200576, 1142549512519680, 7363096858460160, 47326939807481856, 303461150525227008, 1941420131673440256
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (18,-108,216).
Programs
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GAP
List([1..20],n->6^(n-1)*(n^2+21*n+50))/72; # Muniru A Asiru, Oct 18 2018
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Magma
[6^n*(n^2 +23*n +72)/72: n in [0..50]]; // G. C. Greubel, Oct 17 2018
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Maple
seq(coeff(series((1-5*x)^2/(1-6*x)^3,x,n+1), x, n), n = 0 .. 20); # Muniru A Asiru, Oct 18 2018
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Mathematica
Table[6^n*(n^2+23*n+72)/72, {n,0,50}] (* or *) LinearRecurrence[{18,-108, 216}, {1, 8, 61}, 50] (* G. C. Greubel, Oct 17 2018 *) -
PARI
vector(50, n, n--; 6^n*(n^2 +23*n +72)/72) \\ G. C. Greubel, Oct 17 2018
Formula
a(n) = 6^n*(n^2 + 23*n + 72)/72.
G.f.: (1-5*x)^2/(1-6*x)^3.
E.g.f.: (2 + 4*x + x^2)*exp(6*x)/2. - G. C. Greubel, Oct 17 2018
Comments