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%I #10 Nov 15 2022 11:50:23
%S 406,13818,115836,545860,1858290,5124126,12182968,25945416,50745870,
%T 92745730,160386996,264896268,420839146,646725030,965662320,
%U 1406064016,2002403718,2796022026,3835983340,5179983060,6895305186,9059830318,11763094056,15107395800
%N Expansion of 14*x*(29 + 784*x + 1974*x^2 + 784*x^3 + 29*x^4) / (1 - x)^7.
%C Seems to be the second column of A316387.
%H Colin Barker, <a href="/A317982/b317982.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F G.f.: 14*x*(29 + 784*x + 1974*x^2 + 784*x^3 + 29*x^4) / (1 - x)^7.
%F a(n) = 70*n^6 + 210*n^5 + 175*n^4 - 42*n^2 - 7*n.
%F a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
%t LinearRecurrence[{7,-21,35,-35,21,-7,1},{406,13818,115836,545860,1858290,5124126,12182968},30] (* _Harvey P. Dale_, Nov 15 2022 *)
%o (PARI) Vec(14*x*(29 + 784*x + 1974*x^2 + 784*x^3 + 29*x^4) / (1 - x)^7 + O(x^40))
%o (PARI) a(n) = 70*n^6 + 210*n^5 + 175*n^4 - 42*n^2 - 7*n
%Y Cf. A316387, A317981, A317983, A317984.
%K nonn,easy
%O 1,1
%A _Colin Barker_, Aug 13 2018
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