|
%I #2 Mar 30 2012 18:37:20
%S 1,2,6,34,280,3010,39984,634040,11704548,246799212,5856139256,
%T 154509170816,4488522398568,142395677932872,4899139202191216,
%U 181714457372434436,7228856213182113768,307047663830976178304
%N a(n) = coefficient of x^n in the n-th iteration of Sum_{k>=0} x^(2^k), n>=1.
%e Let F(x) = x + x^2 + x^4 + x^8 + x^16 +...+ x^(2^n) +...
%e and define F_{n}(x) = F_{n-1}(F(x)) as the n-th iteration of F(x)
%e then the coefficients in the successive iterations of F(x) begin:
%e F_1: [(1), 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, ...];
%e F_2: [1, (2), 2, 3, 6, 8, 8, 16, 22, 40, 80, 146, 240, 356,...];
%e F_3: [1, 3, (6), 12, 28, 68, 152, 330, 722, 1614, 3680, 8810, ...];
%e F_4: [1, 4, 12, (34), 100, 310, 972, 3012, 9190, 27826, 84192,...];
%e F_5: [1, 5, 20, 75, (280), 1070, 4176, 16449, 64710, 253166, ...];
%e F_6: [1, 6, 30, 141, 650, (3010), 14116, 66972, 319788, 1529230,...];
%e F_7: [1, 7, 42, 238, 1316, 7238, (39984), 222614, 1248304,...];
%e F_8: [1, 8, 56, 372, 2408, 15428, 98728, (634040), 4092964,...];
%e F_9: [1, 9, 72, 549, 4080, 29940, 218688, 1597689, (11704548),...]; ...
%e where the coefficients in parenthesis form the initial terms of this sequence.
%o (PARI) {a(n)=local(G=x,S2=sum(m=0,#binary(n)+1,x^(2^m))+x*O(x^n)); for(i=1,n,G=subst(S2,x,G));polcoeff(G,n)}
%K nonn
%O 1,2
%A _Paul D. Hanna_, Nov 23 2009
|
