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A051608
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a(n) = (3*n+8)!!!/8!!!.
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6
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1, 11, 154, 2618, 52360, 1204280, 31311280, 908027120, 29056867840, 1016990374400, 38645634227200, 1584471003315200, 69716724145868800, 3276686034855833600, 163834301742791680000, 8683217992367959040000, 486260207572605706240000, 28689352246783736668160000
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OFFSET
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0,2
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COMMENTS
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Related to A008544(n+1) ((3*n+2)!!! triple factorials).
Row m=8 of the array A(4; m,n) := ((3*n+m)(!^3))/m(!^3), m >= 0, n >= 0.
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LINKS
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FORMULA
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a(n) = ((3*n+8)(!^3))/8(!^3).
E.g.f.: 1/(1-3*x)^(11/3).
Sum_{n>=0} 1/a(n) = 1 + 9*(9*e)^(1/3)*(Gamma(11/3) - Gamma(11/3, 1/3)). - Amiram Eldar, Dec 23 2022
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MATHEMATICA
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With[{nn = 30}, CoefficientList[Series[1/(1 - 3*x)^(11/3), {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/(1-3*x)^(11/3))) \\ G. C. Greubel, Aug 15 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(1/(1-3*x)^(11/3))); [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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