A242573 - OEIS

%I #6 May 17 2014 19:01:17

%S 1,1,2,6,24,120,702,4445,27812,187911,4154105,226545132,11811552612,

%T 567839904255,26530164469576,1244353584654296,59633342751369016,

%U 2947881116272213508,151083714566902161495,8048911065786420441543,446230730213409483222040

%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,x) = G(n-1, G(1,x)) with G(0,x)=x.

%H Paul D. Hanna, <a href="/A242573/b242573.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,  0,  0,   0,    0,     0,      0,       0,        0,        0, ...];

%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 the main 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. A242574, A242575.

%K nonn

%O 1,3

%A _Paul D. Hanna_, May 17 2014