A062149 - OEIS

%I #28 Sep 08 2022 08:45:03

%S 1,24,432,7200,118800,1995840,34594560,622702080,11675664000,

%T 228324096000,4657811558400,99084354969600,2196369868492800,

%U 50685458503680000,1216451004088320000,30330178368602112000

%N Third column sequence of triangle A062138 (generalized a=5 Laguerre).

%H Indranil Ghosh, <a href="/A062149/b062149.txt">Table of n, a(n) for n = 0..400</a>

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

%F E.g.f.: (1 + 14*x + 21*x^2)/(1 - x)^10.

%F a(n) = A062138(n+2, 2).

%F a(n) = (n+2)!*binomial(n+7, 7)/2!.

%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-2) = (-1)^n*f(n,2,-8), (n >= 2). - _Milan Janjic_, Mar 01 2009

%e a(2) = (2+2)! * binomial(2+7,7) / 2! = (24 * 36) / 2 = 432. - _Indranil Ghosh_, Feb 24 2017

%p a:=n-> (n+2)!*binomial(n+7, 7)/2!: seq(a(n), n=0..22); # _Zerinvary Lajos_, Apr 29 2007

%t Table[(n+2)!*Binomial[n+7,7]/2!,{n,0,15}] (* _Indranil Ghosh_, Feb 24 2017 *)

%o (PARI)a(n)=(n+2)!*binomial(n+7, 7)/2! \\ _Indranil Ghosh_, Feb 24 2017

%o (Python)

%o import math

%o f=math.factorial

%o def C(n, r):return f(n)/f(r)/f(n-r)

%o def A062149(n): return f(n+2)*C(n+7, 7)/f(2) # _Indranil Ghosh_, Feb 24 2017

%o (Magma) [Factorial(n+2)*Binomial(n+7,7)/2: n in [0..20]]; // _G. C. Greubel_, May 12 2018

%Y Cf. A062148.

%K nonn,easy

%O 0,2

%A _Wolfdieter Lang_, Jun 19 2001