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%I #12 Nov 04 2023 05:24:26
%S 0,1,9,53,253,1059,4043,14407,48639,157184,489872,1480608,4358752,
%T 12541184,35364864,97960192,267050240,717619200,1903452160,4989337600,
%U 12937052160,33212530688,84484882432,213090238464,533236219904
%N Convolution of A055853 with A011782.
%C Ninth column of triangle A055587.
%C T(n,7) of array T as in A049600.
%H G. C. Greubel, <a href="/A055854/b055854.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (16,-112,448,-1120,1792,-1792,1024,-256).
%F a(n)= T(n, 7)= A055587(n+7, 8).
%F G.f.: x*(1-x)^7/(1-2*x)^8.
%p seq(coeff(series(x*(1-x)^7/(1-2*x)^8, x, n+1), x, n), n = 0..30); # _G. C. Greubel_, Jan 16 2020
%t CoefficientList[Series[x*(1-x)^7/(1-2*x)^8, {x,0,30}], x] (* _G. C. Greubel_, Jan 16 2020 *)
%t LinearRecurrence[{16,-112,448,-1120,1792,-1792,1024,-256},{0,1,9,53,253,1059,4043,14407,48639,157184},40] (* _Harvey P. Dale_, Nov 04 2023 *)
%o (PARI) my(x='x+O('x^30)); concat([0], Vec(x*(1-x)^7/(1-2*x)^8)) \\ _G. C. Greubel_, Jan 16 2020
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 30); [0] cat Coefficients(R!( x*(1-x)^7/(1-2*x)^8 )); // _G. C. Greubel_, Jan 16 2020
%o (Sage)
%o def A055854_list(prec):
%o P.<x> = PowerSeriesRing(ZZ, prec)
%o return P( x*(1-x)^7/(1-2*x)^8 ).list()
%o A055854_list(30) # _G. C. Greubel_, Jan 16 2020
%Y Cf. A011782, A049600, A055587, A055853.
%K nonn,easy
%O 0,3
%A _Wolfdieter Lang_ May 30 2000
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