%I A075271
%S A075271 1,3,17,211,5793,339491,41326513,10282961907,5181436229441,
%T A075271 5258784071302723,10717167529963833681,43779339268428732008723,
%U A075271 358114286723184561034838497,5862685570087914880854259126371
%N A075271 a(0)=1 and, for n>=1, (BM)a(n)=2a(n-1), where BM is the BinomialMean 
               transform. BM is defined by (BM)a(n)=(M^n)a(0) where (M)a(n) is the 
               mean (a(n)+a(n+1))/2, or, alternatively, by (BM)a(n)=Sum[C(n,k)a(k),
               k=0..n]/(2^n).
%C A075271 The BinomialMean transform of this sequence is given in A075272.
%D A075271 Michael Z. Spivey and Laura L. Steil, The k-Binomial Transforms and the 
               Hankel Transform, Journal of Integer Sequences, Vol. 9 (2006), Article 
               06.1.1.
%e A075271 Given that a(0)=1 and a(1)=3. Then (BM)a(2)=(1+2*3+a(2))/4=2a(1)=6, hence 
               a(2)=17.
%p A075271 iBM:= proc(p) proc (n) option remember; add (2^(k) *p(k) *(-1)^(n-k) 
               *binomial(n,k), k=0..n) end end: aa:='aa': a:= iBM(aa): aa:= n-> 
               `if`(n=0,1, 2*a(n-1)): seq (a(n), n=0..16); [From Alois P. Heinz 
               (heinz(AT)hs-heilbronn.de), Sep 09 2008]
%Y A075271 Sequence in context: A158885 A133991 A009494 this_sequence A072350 A084040 
               A009495
%Y A075271 Adjacent sequences: A075268 A075269 A075270 this_sequence A075272 A075273 
               A075274
%K A075271 eigen,nonn
%O A075271 0,2
%A A075271 John W. Layman (layman(AT)math.vt.edu), Sep 11 2002
%E A075271 More terms from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 09 2008