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A051620
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(4*n+8)(!^4)/8(!^4), related to A034177(n+1) ((4*n+4)(!^4) quartic, or 4-factorials).
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0
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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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Table of n, a(n) for n=0..15.
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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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restart: 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); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 04 2009]
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MATHEMATICA
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s=1; lst={s}; Do[s+=n*s; AppendTo[lst, s], {n, 11, 5!, 4}]; lst [From Vladimir Joseph Stephan Orlovsky, Nov 08 2008]
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CROSSREFS
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Cf. A047053, A007696(n+1), A000407, A034176(n+1), A034177(n+1), A051617-A051622 (rows m=0..10).
Sequence in context: A196716 A086948 A212596 * A144347 A095351 A061065
Adjacent sequences: A051617 A051618 A051619 * A051621 A051622 A051623
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KEYWORD
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easy,nonn
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AUTHOR
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Wolfdieter Lang
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STATUS
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approved
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