OFFSET
0,2
COMMENTS
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.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..378
FORMULA
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
a(n) = (3*n+5)*a(n-1). - R. J. Mathar, Nov 13 2012
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
MATHEMATICA
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 *)
PROG
(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
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
STATUS
approved