A185751 - OEIS

A185751

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

1, 2, 12, 130, 2070, 43771, 1157226, 36768138, 1365331392, 58043143939, 2780443920881, 148205724807504, 8701065456735366, 557920119793398207, 38795723269918254258, 2907928965514543274650, 233727463470863679243682

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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).

LINKS

Table of n, a(n) for n=1..17.

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

Adjacent sequences: A185748 A185749 A185750 * A185752 A185753 A185754

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Feb 01 2011

STATUS

approved