A062260 - OEIS

%I #32 Sep 08 2022 08:45:03

%S 1,21,336,5040,75600,1164240,18627840,311351040,5448643200,

%T 99891792000,1917922406400,38532804710400,809188898918400,

%U 17739910476288000,405483668029440000,9650511299100672000

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

%H Harry J. Smith, <a href="/A062260/b062260.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+12*x+15*x^2)/(1-x)^9.

%F a(n) = A062140(n+2, 2) = (n+2)!*binomial(n+6, 6)/2!.

%F If we define f(n,i,x) = Sum_{k=1..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,-7), (n>=2). - _Milan Janjic_, Mar 01 2009

%F a(n) = binomial(n,6)*(n-4)!/2, n >= 6. - _Zerinvary Lajos_, Jul 07 2009

%p a:=n->sum((n-j)*n!/6!, j=5..n): seq(a(n), n=6..21); # _Zerinvary Lajos_, Apr 29 2007

%t Table[(n + 2)! Binomial[n + 6, 6]/2, {n, 0, 20}] (* _Wesley Ivan Hurt_, Jan 23 2017 *)

%o (Sage) [binomial(n,6)*factorial (n-4)/2 for n in range(6, 22)] # _Zerinvary Lajos_, Jul 07 2009

%o (PARI) { f=1; for (n=0, 100, f*=n + 2; write("b062260.txt", n, " ", f*binomial(n + 6, 6)/2) ) } \\ _Harry J. Smith_, Aug 03 2009

%o (Magma) [Factorial(n+2)*Binomial(n+6, 6)/2: n in [0..30]]; // _G. C. Greubel_, Feb 06 2018

%Y Cf. A001720, A062199.

%K nonn,easy

%O 0,2

%A _Wolfdieter Lang_, Jun 19 2001