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A144690 Limit of the coefficient of x^(2^m+n) in B(x)^(n+1) as m grows, where B(x) = Sum_{k>=0} x^(2^k).

%I A144690 #17 Mar 30 2012 18:37:14
%S A144690 1,2,6,16,130,636,5712,34336,811458,7151380,113034746,1049982792,
%T A144690 25276020640,293841338896,5712436923000,68827002466176,
%U A144690 3739997267623490,60752008945662372,1718332635327516238,26832922324005759560,1099199814287516279394
%N A144690 Limit of the coefficient of x^(2^m+n) in B(x)^(n+1) as m grows, where B(x) = Sum_{k>=0} x^(2^k).
%C A144690 The g.f. of A144691(n) = a(n)/(n+1) appears to have an interesting functional interpretation.
%C A144690 For a fixed n, the sequence of [x^(2^m+n)] B(x)^(n+1), m=0,1,2,... seems to stabilize at m = n + A023416(n). [From _Max Alekseyev_, Dec 19 2011]
%H A144690 Max Alekseyev, <a href="/A144690/b144690.txt">Table of n, a(n) for n = 0..27</a>
%F A144690 a(n) = (n+1)*A144691(n).
%o A144690 (PARI) { a(n) = local(m=n+log(n+.5)\log(2), B=sum(k=0,m,x^(2^k)));if(n<0, 0, polcoeff((B+O(x^(2^m+n+1)))^(n+1),2^m+n)) }
%Y A144690 Cf. A007178, A144691, A144692, A135068, A135069, A135070, A135071.
%K A144690 nonn
%O A144690 0,2
%A A144690 _Paul D. Hanna_, Oct 10 2008
%E A144690 a(14), a(15) corrected and a(16)-a(23) added by _Max Alekseyev_, May 03 2011
%E A144690 a(24)-a(27) in b-file from _Max Alekseyev_, Dec 19 2011