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A185751
a(n) equals the coefficient of x^(2n-1) in the n-th iteration of x/(1-x^2) for n>=1.
1
1, 2, 12, 130, 2070, 43771, 1157226, 36768138, 1365331392, 58043143939, 2780443920881, 148205724807504, 8701065456735366, 557920119793398207, 38795723269918254258, 2907928965514543274650, 233727463470863679243682
OFFSET
1,2
COMMENTS
Compare a(n) to n^(2n-2), which is the coefficient of x^(2n-1) in the n-th iteration of x/(1-x).
EXAMPLE
The coefficients of x^(2k-1), k>=1, in the n-th iterations of x/(1-x^2) begin:
n=1: [(1), 1, 1, 1, 1, 1, 1, 1, ...];
n=2: [1,(2), 5, 13, 34, 89, 233, 610, 1597, ...];
n=3: [1, 3,(12), 51, 221, 965, 4227, 18540, ...];
n=4: [1, 4, 22,(130), 789, 4848, 29975, 185953, ...];
n=5: [1, 5, 35, 265,(2070), 16420, 131353, 1055966, ...];
n=6: [1, 6, 51, 471, 4501,(43771), 429939, 4249026, ...];
n=7: [1, 7, 70, 763, 8624, 99344,(1157226), 13575289, ...];
n=8: [1, 8, 92, 1156, 15086, 200880, 2707230,(36768138), ...]; ...
coefficients in parenthesis form the initial terms of this sequence.
PROG
(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)}
CROSSREFS
Cf. A185752.
Sequence in context: A303926 A214759 A365601 * A090361 A377360 A258467
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Feb 01 2011
STATUS
approved