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A051621
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a(n) = (4*n+9)(!^4)/9(!^4), related to A007696(n+1) ((4*n+1)(!^4) quartic, or 4-factorials).
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4
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1, 13, 221, 4641, 116025, 3364725, 111035925, 4108329225, 168441498225, 7579867420125, 371413503586125, 19684915690064625, 1122040194333683625, 68444451854354701125, 4448889370533055573125, 306973366566780834545625
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OFFSET
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0,2
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COMMENTS
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Row m=9 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+9)(!^4))/9(!^4) = A007696(n+3)/(5*9).
E.g.f.: 1/(1-4*x)^(13/4).
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MATHEMATICA
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With[{nn = 30}, CoefficientList[Series[1/(1 - 4*x)^(13/4), {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)^(13/4))) \\ G. C. Greubel, Aug 15 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(1/(1-4*x)^(13/4))); [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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