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A051620
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a(n) = (4*n+8)(!^4)/8(!^4), related to A034177(n+1) ((4*n+4)(!^4) quartic, or 4-factorials).
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5
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1, 12, 192, 3840, 92160, 2580480, 82575360, 2972712960, 118908518400, 5231974809600, 251134790860800, 13059009124761600, 731304510986649600, 43878270659198976000, 2808209322188734464000, 190958233908833943552000
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OFFSET
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0,2
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COMMENTS
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Row m=8 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+8)(!^4))/8(!^4) = A034177(n+2)/8.
E.g.f.: 1/(1-4*x)^3.
G.f.: G(0)/2, where G(k)= 1 + 1/(1 - 2*x/(2*x + 1/(2*k+6)/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, Jun 02 2013
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MAPLE
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G(x):=(1-4*x)^(n-4): f[0]:=G(x): for n from 1 to 29 do f[n]:=diff(f[n-1], x) od:x:=0:seq(f[n], n=0..15); # Zerinvary Lajos, Apr 04 2009
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MATHEMATICA
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With[{nn=20}, CoefficientList[Series[1/(1-4*x)^3, {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Mar 10 2017 *)
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PROG
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(PARI) x='x+O('x^30); Vec(serlaplace(1/(1-4*x)^(12/4))) \\ G. C. Greubel, Aug 15 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(1/(1-4*x)^(12/4))); [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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