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A085351 Expansion of (1-3*x)/((1-4*x)*(1-5*x)). 4

%I

%S 1,6,34,186,994,5226,27154,139866,715714,3644106,18482674,93461946,

%T 471504034,2374297386,11938595794,59961414426,300880813954,

%U 1508699037066,7560675054514,37872094749306,189635351653474

%N Expansion of (1-3*x)/((1-4*x)*(1-5*x)).

%C Binomial transform of A085350. Second binomial transform of poly-Bernoulli numbers A027649.

%H Colin Barker, <a href="/A085351/b085351.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (9,-20).

%F G.f.: (1-3*x)/((1-4*x)*(1-5*x)).

%F a(n) = 2*5^n - 4^n.

%F a(n) = 9*a(n-1) - 20*a(n-2) for n>1. - _Colin Barker_, Jun 25 2020

%t CoefficientList[Series[(1-3x)/((1-4x)(1-5x)),{x,0,20}],x] (* or *) LinearRecurrence[{9,-20},{1,6},30] (* _Harvey P. Dale_, Jan 07 2022 *)

%o (PARI) Vec((1 - 3*x) / ((1 - 4*x)*(1 - 5*x)) + O(x^25)) \\ _Colin Barker_, Jun 25 2020

%Y Cf. A027649, A085350, A085352.

%K easy,nonn

%O 0,2

%A _Paul Barry_, Jun 24 2003

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Last modified February 3 21:17 EST 2023. Contains 360045 sequences. (Running on oeis4.)