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A323223
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a(n) = [x^n] x/((1 - x)*(1 - 4*x)^(5/2)).
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2
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0, 1, 11, 81, 501, 2811, 14823, 74883, 366603, 1752273, 8218733, 37964449, 173172249, 781607349, 3496163949, 15517771749, 68412846069, 299828796219, 1307168814519, 5672308893819, 24511334499219, 105519144602439, 452695473616239, 1936085243038839, 8256615564926439
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = ((5*n + 1)*a(n-1) - (4*n + 2)*a(n-2))/(n - 1) for n >= 2.
a(n) = -(-4)^n*binomial(-5/2, n)*hypergeom([1, n+5/2], [n+1], 4) - i*sqrt(3)/27.
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MAPLE
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A323223List := proc(len) local ogf, ser; ogf := (1 - 4*x)^(-5/2)*x/(1 - x);
ser := series(ogf, x, (n+1)*len+1); seq(coeff(ser, x, j), j=0..len) end:
A323223List(24);
# Alternative:
a := proc(n) option remember; `if`(n<2, n, ((5*n+1)*a(n-1)-(4*n+2)*a(n-2))/(n-1)) end: seq(a(n), n=0..24);
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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