A051605 a(n) = (3*n+5)!!!/5!!!.

1, 8, 88, 1232, 20944, 418880, 9634240, 250490240, 7264216960, 232454942720, 8135922995200, 309165073817600, 12675768026521600, 557733793166950400, 26213488278846668800, 1310674413942333440000, 69465743938943672320000, 3890081660580845649920000

Offset: 0

Author

Wolfdieter Lang

Keywords

• easy
• nonn

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

Crossrefs

Cf. A032031, A007559(n+1), A034000(n+1), A034001(n+1), A051604 (rows m=0..4).

Programs

Magma

m:=30; R:=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

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 *)

PARI

x='x+O('x^30); Vec(serlaplace(1/(1-3*x)^(8/3))) \\ G. C. Greubel, Aug 15 2018

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