OFFSET
0,2
COMMENTS
Related to A007559(n+1) ((3*n+1)!!! triple factorials).
Row m=7 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+7)(!^3))/7(!^3).
E.g.f.: 1/(1-3*x)^(10/3).
Sum_{n>=0} 1/a(n) = 1 + 9*(3*e)^(1/3)*(Gamma(10/3) - Gamma(10/3, 1/3)). - Amiram Eldar, Dec 23 2022
MATHEMATICA
With[{nn = 30}, CoefficientList[Series[1/(1 - 3*x)^(10/3), {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)^(10/3))) \\ G. C. Greubel, Aug 15 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(1/(1-3*x)^(10/3))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Aug 15 2018
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
STATUS
approved