A051607 a(n) = (3*n+7)!!!/7!!!.

1, 10, 130, 2080, 39520, 869440, 21736000, 608608000, 18866848000, 641472832000, 23734494784000, 949379791360000, 40823331028480000, 1877873227310080000, 92015788138193920000, 4784820983186083840000, 263165154075234611200000, 15263578936363607449600000

Offset: 0

Author

Wolfdieter Lang

Keywords

• easy
• nonn

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

Crossrefs

Cf. A032031, A007559(n+1), A034000(n+1), A034001(n+1), A051604, A051605, A051606, A051608, A051609 (rows m=0..9).

Programs

Magma

m:=30; R:=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

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 *)

PARI

x='x+O('x^30); Vec(serlaplace(1/(1-3*x)^(10/3))) \\ G. C. Greubel, Aug 15 2018

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