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A316457 Expansion of x*(31 + 326*x + 336*x^2 + 26*x^3 + x^4) / (1 - x)^6. 4

%I #10 Aug 18 2018 11:23:32

%S 31,512,2943,10624,29375,68256,140287,263168,459999,760000,1199231,

%T 1821312,2678143,3830624,5349375,7315456,9821087,12970368,16879999,

%U 21680000,27514431,34542112,42937343,52890624,64609375,78318656,94261887,112701568,133919999

%N Expansion of x*(31 + 326*x + 336*x^2 + 26*x^3 + x^4) / (1 - x)^6.

%C Seems to be the first column of A316349.

%H Colin Barker, <a href="/A316457/b316457.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).

%F G.f.: x*(31 + 326*x + 336*x^2 + 26*x^3 + x^4) / (1 - x)^6.

%F a(n) = 6*n^5 + 15*n^4 + 10*n^3.

%F a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.

%o (PARI) Vec(x*(31 + 326*x + 336*x^2 + 26*x^3 + x^4) / (1 - x)^6 + O(x^40))

%o (PARI) a(n) = 6*n^5 + 15*n^4 + 10*n^3

%Y Cf. A316349, A316458, A316459.

%K nonn,easy

%O 1,1

%A _Colin Barker_, Aug 12 2018

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