A185751 - OEIS

%I #6 Mar 30 2012 18:37:26

%S 1,2,12,130,2070,43771,1157226,36768138,1365331392,58043143939,

%T 2780443920881,148205724807504,8701065456735366,557920119793398207,

%U 38795723269918254258,2907928965514543274650,233727463470863679243682

%N a(n) equals the coefficient of x^(2n-1) in the n-th iteration of x/(1-x^2) for n>=1.

%C  Compare a(n) to n^(2n-2), which is the coefficient of x^(2n-1) in the n-th iteration of x/(1-x).

%e The coefficients of x^(2k-1), k>=1, in the n-th iterations of x/(1-x^2) begin:

%e n=1: [(1), 1, 1, 1, 1, 1, 1, 1, ...];

%e n=2: [1,(2), 5, 13, 34, 89, 233, 610, 1597, ...];

%e n=3: [1, 3,(12), 51, 221, 965, 4227, 18540, ...];

%e n=4: [1, 4, 22,(130), 789, 4848, 29975, 185953, ...];

%e n=5: [1, 5, 35, 265,(2070), 16420, 131353, 1055966, ...];

%e n=6: [1, 6, 51, 471, 4501,(43771), 429939, 4249026, ...];

%e n=7: [1, 7, 70, 763, 8624, 99344,(1157226), 13575289, ...];

%e n=8: [1, 8, 92, 1156, 15086, 200880, 2707230,(36768138), ...]; ...

%e coefficients in parenthesis form the initial terms of this sequence.

%o (PARI) {a(n)=local(A=x,G=x/(1-x^2)); for(i=1,n, A=subst(G, x, A+x*O(x^(2*n)))); polcoeff(A, 2*n-1)}

%Y Cf. A185752.

%K nonn

%O 1,2

%A _Paul D. Hanna_, Feb 01 2011