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A051617
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a(n) = (4*n+5)(!^4)/5(!^4), related to A007696(n+1) ((4*n+1)(!^4) quartic, or 4-factorials).
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9
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1, 9, 117, 1989, 41769, 1044225, 30282525, 999323325, 36974963025, 1515973484025, 68218806781125, 3342721532275125, 177164241210581625, 10098361749003152625, 616000066689192310125, 40040004334797500158125
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OFFSET
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0,2
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COMMENTS
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Row m=5 of the array A(5; m,n) := ((4*n+m)(!^4))/m(!^4), m >= 0, n >= 0.
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LINKS
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FORMULA
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a(n) = ((4*n+5)(!^4))/5(!^4).
E.g.f.: 1/(1-4*x)^(9/4).
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MATHEMATICA
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With[{nn = 30}, CoefficientList[Series[1/(1 - 4*x)^(9/4), {x, 0, nn}], x]*Range[0, nn]!] (* G. C. Greubel, Aug 15 2018 *)
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PROG
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(PARI) x='x+O('x^30); Vec(serlaplace(1/(1-4*x)^(9/4))) \\ G. C. Greubel, Aug 15 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(1/(1-4*x)^(9/4))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Aug 15 2018
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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