A062262 - OEIS

%I #16 Sep 08 2022 08:45:03

%S 1,45,1350,34650,831600,19459440,454053600,10702692000,256864608000,

%T 6307453152000,158947819430400,4118193503424000,109818493424640000,

%U 3015784780968960000,85303626661693440000

%N Fifth (unsigned) column sequence of triangle A062140 (generalized a=4 Laguerre).

%H Harry J. Smith, <a href="/A062262/b062262.txt">Table of n, a(n) for n = 0..100</a>

%H <a href="/index/La#Laguerre">Index entries for sequences related to Laguerre polynomials</a>

%F E.g.f.: (1+32*x+168*x^2+224*x^3+70*x^4)/(1-x)^13.

%F a(n) = A062140(n+4, 4).

%F a(n) = (n+4)!*binomial(n+8, 8)/4!.

%F If we define f(n,i,x)= Sum_{k=i..n} Sum_{j=i..k} binomial(k,j)* Stirling1(n,k)*Stirling2(j,i)*x^(k-j) then a(n-4) = (-1)^n*f(n,4,-9), (n>=4). - _Milan Janjic_, Mar 01 2009

%t Table[(n+4)!*Binomial[n+8, 8]/4!, {n, 0, 30}] (* _G. C. Greubel_, May 13 2018 *)

%o (PARI) { f=6; for (n=0, 100, f*=n + 4; write("b062262.txt", n, " ", f*binomial(n + 8, 8)/24) ) } \\ _Harry J. Smith_, Aug 03 2009

%o (Magma) [Factorial(n+4)*Binomial(n+8,8)/24: n in [0..30]]; // _G. C. Greubel_, May 13 2018

%Y Cf. A001720, A062199, A062260, A062261.

%K nonn,easy

%O 0,2

%A _Wolfdieter Lang_, Jun 19 2001