A051608 a(n) = (3*n+8)!!!/8!!!.

1, 11, 154, 2618, 52360, 1204280, 31311280, 908027120, 29056867840, 1016990374400, 38645634227200, 1584471003315200, 69716724145868800, 3276686034855833600, 163834301742791680000, 8683217992367959040000, 486260207572605706240000, 28689352246783736668160000

Offset: 0

Author

Wolfdieter Lang

Keywords

• easy
• nonn

Comments

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.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..377

Crossrefs

Cf. A032031, A007559(n+1), A034000(n+1), A034001(n+1), A051604, A051605, A051606, A051607, A051609 (rows m=0..9).

Cf. A008544.

Programs

Magma

m:=30; R:=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

Mathematica

With[{nn = 30}, CoefficientList[Series[1/(1 - 3*x)^(11/3), {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)^(11/3))) \\ G. C. Greubel, Aug 15 2018

Formula

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