This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A129953 #20 Oct 04 2024 08:52:57
%S A129953 0,1,4,10,24,56,128,288,640,1408,3072,6656,14336,30720,65536,139264,
%T A129953 294912,622592,1310720,2752512,5767168,12058624,25165824,52428800,
%U A129953 109051904,226492416,469762048,973078528,2013265920,4160749568
%N A129953 First differences of A129952.
%H A129953 Vincenzo Librandi, <a href="/A129953/b129953.txt">Table of n, a(n) for n = 0..1000</a>
%H A129953 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,-4).
%F A129953 a(n) = A129952(n+1) - A129952(n).
%F A129953 a(n) = A087447(n) for n > 0.
%F A129953 a(0) = 0, a(1) = 1; for n > 1, a(n) = (n+2)*2^(n-2).
%F A129953 G.f.: x*(1-2*x^2)/(1-2*x)^2.
%o A129953 (Magma) m:=16; S:=&cat[ [ 1, 2*i ]: i in [0..m] ]; T:=[ &+[ Binomial(j-1, k-1)*S[k]: k in [1..j] ]: j in [1..2*m] ]; [ T[n+1]-T[n]: n in[1..2*m-1] ]; // _Klaus Brockhaus_, Jun 17 2007
%o A129953 (PARI) {m=29; print1(0, ",", 1, ","); for(n=2, m, print1((n+2)*2^(n-2), ","))} \\ _Klaus Brockhaus_, Jun 17 2007
%o A129953 (Python)
%o A129953 def A129953(n): return n+2<<n-2 if n>1 else n # _Chai Wah Wu_, Oct 03 2024
%Y A129953 Cf. A129952, A087447.
%K A129953 nonn,easy
%O A129953 0,3
%A A129953 _Paul Curtz_, Jun 10 2007
%E A129953 Edited and extended by _Klaus Brockhaus_, Jun 17 2007