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A370051 Expansion of (1-5*x+6*x^2-x^3)/(1-9*x+28*x^2-35*x^3+15*x^4-x^5).

%I A370051 #17 Feb 20 2024 14:42:32
%S A370051 1,4,14,48,165,572,2002,7071,25176,90251,325358,1178291,4282811,
%T A370051 15612092,57040186,208772476,765186422,2807556411,10309833845,
%U A370051 37883902913,139275229088,512223805060,1884404481767,6934058102453,25519786076294
%N A370051 Expansion of (1-5*x+6*x^2-x^3)/(1-9*x+28*x^2-35*x^3+15*x^4-x^5).
%C A370051 In Pascal's triangle, subtract the 6th column to the left of the central column from the 2nd column.
%H A370051 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (9,-28,35,-15,1).
%F A370051 a(n) = 9*a(n-1) - 28*a(n-2) + 35*a(n-3) - 15*a(n-4) + a(n-5); a(0) = 1, a(1) = 4, a(2) = 14, a(3) = 48, a(4) = 165.
%e A370051 a(0) = binomial(2,0);
%e A370051 a(1) = binomial(4,1);
%e A370051 a(2) = binomial(6,2) - binomial(6,0);
%e A370051 a(3) = binomial(8,3) - binomial(8,1);
%e A370051 a(4) = binomial(10,4) - binomial(10,2).
%t A370051 LinearRecurrence[{9, -28, 35, -15, 1}, {1, 4, 14, 48, 165}, 30] (* _Paolo Xausa_, Feb 20 2024 *)
%Y A370051 Cf. A007318, A211216, A224422, A221863, A122588.
%K A370051 nonn,easy
%O A370051 0,2
%A A370051 _Peter Morris_, Feb 08 2024