A053103 - OEIS

A053103

a(n) = ((6*n+10)(!^6))/10(!^6), related to A034724 (((6*n+4)(!^6))/4 sextic, or 6-factorials).

%I #16 Sep 08 2022 08:45:00

%S 1,16,352,9856,335104,13404160,616591360,32062750720,1859639541760,

%T 119016930672640,8331185147084800,633170071178444800,

%U 51919945836632473600,4568955233623657676800,429481791960623821619200

%N a(n) = ((6*n+10)(!^6))/10(!^6), related to A034724 (((6*n+4)(!^6))/4 sextic, or 6-factorials).

%C Row m=10 of the array A(7; m,n) := ((6*n+m)(!^6))/m(!^6), m >= 0, n >= 0.

%H G. C. Greubel, <a href="/A053103/b053103.txt">Table of n, a(n) for n = 0..343</a>

%F a(n) = ((6*n+10)(!^6))/10(!^6) = A034724(n+2)/10.

%F E.g.f.: 1/(1-6*x)^(8/3).

%t s=1;lst={s};Do[s+=n*s;AppendTo[lst, s], {n, 15, 5!, 6}];lst (* _Vladimir Joseph Stephan Orlovsky_, Nov 08 2008 *)

%t With[{nn = 30}, CoefficientList[Series[1/(1 - 6*x)^(16/6), {x, 0, nn}], x]*Range[0, nn]!] (* _G. C. Greubel_, Aug 16 2018 *)

%o (PARI) x='x+O('x^30); Vec(serlaplace(1/(1-6*x)^(8/3))) \\ _G. C. Greubel_, Aug 16 2018

%o (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(1/(1-6*x)^(8/3))); [Factorial(n-1)*b[n]: n in [1..m]]; // _G. C. Greubel_, Aug 16 2018

%Y Cf. A047058, A008542(n+1), A034689(n+1), A034723(n+1), A034724(n+1), A034787(n+1), A034788(n+1), A053100, A053101, A053102, this sequence (rows m=0..10).

%K easy,nonn

%O 0,2

%A _Wolfdieter Lang_