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A051605
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a(n) = (3*n+5)!!!/5!!!.
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9
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1, 8, 88, 1232, 20944, 418880, 9634240, 250490240, 7264216960, 232454942720, 8135922995200, 309165073817600, 12675768026521600, 557733793166950400, 26213488278846668800, 1310674413942333440000, 69465743938943672320000, 3890081660580845649920000
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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=5 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+5)(!^3))/5(!^3).
E.g.f.: 1/(1-3*x)^(8/3).
a(n) = 3^n*(n+5/3)!/(5/3)!. - Paul Barry, Sep 04 2005
Sum_{n>=0} 1/a(n) = 1 + 3*(9*e)^(1/3)*(Gamma(8/3) - Gamma(8/3, 1/3)). - Amiram Eldar, Dec 23 2022
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MATHEMATICA
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RecurrenceTable[{a[0]==1, a[n]==(3n+5)a[n-1]}, a, {n, 20}] (* Harvey P. Dale, Oct 19 2013 *)
With[{nn = 30}, CoefficientList[Series[1/(1 - 3*x)^(8/3), {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)^(8/3))) \\ G. C. Greubel, Aug 15 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(1/(1-3*x)^(8/3))); [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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