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A051622
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a(n) = (4*n+10)(!^4)/10(!^4), related to A000407 ((4*n+2)(!^4) quartic, or 4-factorials).
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8
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1, 14, 252, 5544, 144144, 4324320, 147026880, 5587021440, 234654900480, 10794125422080, 539706271104000, 29144138639616000, 1690360041097728000, 104802322548059136000, 6916953288171902976000, 484186730172033208320000
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OFFSET
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0,2
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COMMENTS
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Row m=10 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+10)(!^4))/10(!^4) = A000407(n+2)/(6*10).
E.g.f.: 1/(1-4*x)^(7/2).
G.f.: G(0)/2, where G(k)= 1 + 1/(1 - 2*x/(2*x + 1/(2*k+7)/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, Jun 02 2013
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MAPLE
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MATHEMATICA
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With[{nn = 30}, CoefficientList[Series[1/(1 - 4*x)^(7/2), {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)^(14/4))) \\ G. C. Greubel, Aug 15 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(1/(1-4*x)^(14/4))); [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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