A055853 - OEIS

%I #10 Sep 08 2022 08:45:01

%S 0,1,8,43,190,743,2668,8989,28814,88720,264224,765088,2162624,5986304,

%T 16268800,43499264,114629120,298147840,766361600,1948794880,

%U 4907171840,12245598208,30305419264,74425892864,181481635840,439603953664

%N Convolution of A055852 with A011782.

%C Eighth column of triangle A055587.

%C T(n,6) of array T as in A049600.

%H G. C. Greubel, <a href="/A055853/b055853.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (14,-84,280,-560,672,-448,128).

%F a(n) = T(n, 6)= A055587(n+6, 7).

%F G.f.: x*(1-x)^6/(1-2*x)^7.

%p seq(coeff(series(x*(1-x)^6/(1-2*x)^7, x, n+1), x, n), n = 0..30); # _G. C. Greubel_, Jan 16 2020

%t CoefficientList[Series[x*(1-x)^6/(1-2*x)^7, {x,0,30}], x] (* _G. C. Greubel_, Jan 16 2020 *)

%o (PARI) my(x='x+O('x^30)); concat([0], Vec(x*(1-x)^6/(1-2*x)^7)) \\ _G. C. Greubel_, Jan 16 2020

%o (Magma) R<x>:=PowerSeriesRing(Integers(), 30); [0] cat Coefficients(R!( x*(1-x)^6/(1-2*x)^7 )); // _G. C. Greubel_, Jan 16 2020

%o (Sage)

%o def A055853_list(prec):

%o     P.<x> = PowerSeriesRing(ZZ, prec)

%o     return P( x*(1-x)^6/(1-2*x)^7 ).list()

%o A055853_list(30) # _G. C. Greubel_, Jan 16 2020

%Y Cf. A011782, A049600, A055587, A055852.

%K nonn,easy

%O 0,3

%A _Wolfdieter Lang_ May 30 2000