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A245565 a(n) = Product_{i in row n of A245562} Pell(i+1).

%I A245565 #16 Sep 08 2014 10:39:58
%S A245565 1,2,2,5,2,4,5,12,2,4,4,10,5,10,12,29,2,4,4,10,4,8,10,24,5,10,10,25,
%T A245565 12,24,29,70,2,4,4,10,4,8,10,24,4,8,8,20,10,20,24,58,5,10,10,25,10,20,
%U A245565 25,60,12,24,24,60,29,58,70,169,2,4,4,10,4,8,10,24,4,8,8,20,10,20,24,58,4,8,8,20,8,16
%N A245565 a(n) = Product_{i in row n of A245562} Pell(i+1).
%C A245565 This is the Run Length Transform of S(n) = Pell(n+1) (cf. A000129).
%C A245565 The Run Length Transform of a sequence {S(n), n>=0} is defined to be the sequence {T(n), n>=0} given by T(n) = Product_i S(i), where i runs through the lengths of runs of 1's in the binary expansion of n. E.g. 19 is 10011 in binary, which has two runs of 1's, of lengths 1 and 2. So T(19) = S(1)*S(2). T(0)=1 (the empty product).
%H A245565 Alois P. Heinz, <a href="/A245565/b245565.txt">Table of n, a(n) for n = 0..8191</a>
%p A245565 A000129 := proc(n) option remember; if n <=1 then n; else 2*A000129(n-1)+A000129(n-2); fi; end;
%p A245565 ans:=[];
%p A245565 for n from 0 to 100 do lis:=[]; t1:=convert(n,base,2); L1:=nops(t1);
%p A245565 out1:=1; c:=0;
%p A245565 for i from 1 to L1 do
%p A245565    if out1 = 1 and t1[i] = 1 then out1:=0; c:=c+1;
%p A245565    elif out1 = 0 and t1[i] = 1 then c:=c+1;
%p A245565    elif out1 = 1 and t1[i] = 0 then c:=c;
%p A245565    elif out1 = 0 and t1[i] = 0 then lis:=[c,op(lis)]; out1:=1; c:=0;
%p A245565    fi;
%p A245565    if i = L1 and c>0 then lis:=[c,op(lis)]; fi;
%p A245565                    od:
%p A245565 a:=mul(A000129(i+1), i in lis);
%p A245565 ans:=[op(ans),a];
%p A245565 od:
%p A245565 ans;
%Y A245565 Cf. A245562, A000129, A001045, A071053, A245564.
%K A245565 nonn,base
%O A245565 0,2
%A A245565 _N. J. A. Sloane_, Aug 10 2014; revised Sep 05 2014