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Binomial transform of A010688.
4

%I #16 Feb 04 2024 13:16:35

%S 1,8,16,32,64,128,256,512,1024,2048,4096,8192,16384,32768,65536,

%T 131072,262144,524288,1048576,2097152,4194304,8388608,16777216,

%U 33554432,67108864,134217728,268435456,536870912,1073741824,2147483648,4294967296,8589934592

%N Binomial transform of A010688.

%C Hankel transform is := 1,-48,0,0,0,0,0,0,0,...

%H Colin Barker, <a href="/A146541/b146541.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (2).

%F a(0)=1, a(n) = 2^(n+2) for n>0.

%F a(n) = Sum_{k, 0..n} A109466(n,k)*A146534(k).

%F a(n) = A132479(n), n>1. - _R. J. Mathar_, Nov 02 2008

%F G.f.: (1+6*x) / (1-2*x). - _Colin Barker_, Mar 17 2016

%t Join[{1},2^Range[3,40]] (* _Harvey P. Dale_, Feb 28 2016 *)

%o (PARI) Vec((1+6*x)/(1-2*x) + O(x^50)) \\ _Colin Barker_, Mar 17 2016

%Y Cf. A000007, A011782, A000079, A003945, A046055, A146523, A082505, A135092.

%Y Essentially the same as A132479, A077552, A020707.

%K nonn,easy

%O 0,2

%A _Philippe Deléham_, Oct 31 2008

%E Corrected and extended by _Harvey P. Dale_, Feb 28 2016