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A132364
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Expansion of 1/(1-x^2*c(x)), c(x) the g.f. of A000108.
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6
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1, 0, 1, 1, 3, 7, 20, 59, 184, 593, 1964, 6642, 22845, 79667, 281037, 1001092, 3595865, 13009673, 47366251, 173415176, 638044203, 2357941142, 8748646386, 32576869203, 121701491701, 456012458965, 1713339737086
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OFFSET
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0,5
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COMMENTS
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LINKS
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FORMULA
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a(0)=1, a(n) = Sum_{k=0..floor(n/2)} (k/(n-k))*C(2n-3k-1,n-2k)), n>0 .
Conjecture: +(-n+1)*a(n) +(5*n-11)*a(n-1) +2*(-2*n+5)*a(n-2) +(-n+1)*a(n-3) +2*(2*n-5)*a(n-4)=0. - R. J. Mathar, Aug 28 2015
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MATHEMATICA
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a[0] := 1; a[n_] := Sum[(k/(n - k))*Binomial[2*n - 3*k - 1, n - 2*k], {k, 0, Floor[n/2]}]; Table[a[n], {n, 0, 25}] (* G. C. Greubel, Oct 19 2016 *)
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PROG
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(PARI) c(x) = (1 - sqrt(1 - 4*x)) / (2*x); \\ A000108
my(x='x+O('x^30)); Vec(1/(1-x^2*c(x))) \\ Michel Marcus, Nov 13 2022
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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