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 A129953 First differences of A129952. 5

%I

%S 0,1,4,10,24,56,128,288,640,1408,3072,6656,14336,30720,65536,139264,

%T 294912,622592,1310720,2752512,5767168,12058624,25165824,52428800,

%U 109051904,226492416,469762048,973078528,2013265920,4160749568

%N First differences of A129952.

%C a(n) = A129952(n+1) - A129952(n).

%C a(n) = A087447(n) for n > 0.

%H Vincenzo Librandi, <a href="/A129953/b129953.txt">Table of n, a(n) for n = 0..1000</a>

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

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

%o (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 (PARI) {m=29; print1(0, ",", 1, ","); for(n=2, m, print1((n+2)*2^(n-2), ","))} /* Klaus Brockhaus, Jun 17 2007 */

%Y Cf. A129952, A087447.

%K nonn

%O 0,3

%A _Paul Curtz_, Jun 10 2007

%E Edited and extended by _Klaus Brockhaus_, Jun 17 2007

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