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%I #5 May 17 2014 19:09:11
%S 1,3,12,65,464,4235,48000,658197,10676571,200994145,4321369524,
%T 104676808756,2824120458186,84038944594677,2735391623889696,
%U 96690702098948611,3688764754855986702,151064345601782722492,6609564176073032406148,307682727619722793499662
%N a(n) = [x^n] G(n+1,x) where G(n,x) is the n-th iteration of G(1,x) = x/(1-x+x^2), so that G(n+1,x) = G(n, G(1,x)) with G(0,x)=x.
%H Paul D. Hanna, <a href="/A242575/b242575.txt">Table of n, a(n) for n = 1..200</a>
%e Given x/(1-x+x^2) = x + x^2 - x^4 - x^5 + x^7 + x^8 - x^10 - x^11 + x^13 +...
%e form a table of coefficients in the iterations of x/(1-x+x^2) like so:
%e [1, 1, 0, -1, -1, 0, 1, 1, 0, -1, ...];
%e [1, 2, 2, -1, -8, -15, -10, 22, 79, 112, ...];
%e [1, 3, 6, 6, -11, -73, -201, -309, 37, 1913, ...];
%e [1, 4, 12, 26, 24, -116, -808, -3000, -7566, -9882, ...];
%e [1, 5, 20, 65, 155, 120, -1379, -10761, -51202, -183269, ...];
%e [1, 6, 30, 129, 464, 1225, 702, -18978, -169139, -994138, ...];
%e [1, 7, 42, 224, 1057, 4235, 12411, 4445, -301321, -3076795, ...];
%e [1, 8, 56, 356, 2064, 10752, 48000, 156416, 27812, -5458012, ...];
%e [1, 9, 72, 531, 3639, 23064, 132633, 658197, 2388060, 187911, ...];
%e [1, 10, 90, 755, 5960, 44265, 306742, 1942198, 10676571, 43159172, ...]; ...
%e then this sequence forms a diagonal in the above table.
%o (PARI) {a(n)=local(A=x, G=x/(1-x+x^2)); for(i=1, n+1, A=subst(G, x, A+x*O(x^(n)))); polcoeff(A, n)}
%o for(n=1,30,print1(a(n),", "))
%Y Cf. A242573, A242574.
%K nonn
%O 1,2
%A _Paul D. Hanna_, May 17 2014
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