A051604 a(n) = (3*n+4)!!!/4!!!.

1, 7, 70, 910, 14560, 276640, 6086080, 152152000, 4260256000, 132067936000, 4490309824000, 166141463488000, 6645658539520000, 285763317199360000, 13145112591170560000, 644110516967357440000, 33493746882302586880000, 1842156078526642278400000

Offset: 0

Author

Wolfdieter Lang

Keywords

• easy
• nonn

Comments

Related to A007559(n+1) ((3*n+1)!!! triple factorials).

Row m=4 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). (rows m=0..3).

Programs

Magma

m:=30; R:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(1/(1-3*x)^(7/3))); [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)^(7/3), {x, 0, nn}], x]* Range[0,nn]! ] (* G. C. Greubel, Aug 15 2018 *)
With[{c=Times@@Range[4,1,-3]},Table[(Times@@Range[3n+4,1,-3])/c,{n,0,20}]] (* Harvey P. Dale, Feb 06 2023 *)

PARI

x='x+O('x^30); Vec(serlaplace(1/(1-3*x)^(7/3))) \\ G. C. Greubel, Aug 15 2018

Formula

a(n) = ((3*n+4)(!^3))/4(!^3).

E.g.f.: 1/(1-3*x)^(7/3).

Sum_{n>=0} 1/a(n) = 1 + 3*(3*e)^(1/3)*(Gamma(7/3) - Gamma(7/3, 1/3)). - Amiram Eldar, Dec 23 2022