A380493 - OEIS

%I #10 Jan 25 2025 11:27:21

%S 1,6,57,748,12585,259026,6315001,178134552,5711078673,205209960670,

%T 8171229107481,357235056697476,17014791129640057,877089297426429738,

%U 48657292133825026905,2890717184573264397616,183125115830192864360481,12323226433255671469949622

%N a(n) = n! * Sum_{k=0..n} binomial(2*n+3,k)/(n-k)!.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Laguerre_polynomials">Laguerre polynomials</a>

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

%F a(n) = n! * LaguerreL(n, n+3, -1).

%F a(n) = n! * [x^n] exp(x/(1 - x))/(1 - x)^(n+4).

%o (PARI) a(n) = n!*pollaguerre(n, n+3, -1);

%Y Cf. A082545, A152059, A251568, A293985, A343832, A380491, A380492.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Jan 25 2025