A332695 - OEIS

%I #17 Feb 05 2021 08:56:35

%S 1,5,98,3234,149784,8927880,650696400,56061791856,5574017768832,

%T 628158472212096,79123082415148800,11015976349601752320,

%U 1679832851707998600192,278440504042352431942656,49846084962712218734045184,9584526091509128369970432000,1970059291620925696814892810240

%N a(n) = (-1)^n * n! * Laguerre(n, 6*n).

%C For m > 4, (-1)^n * n! * Laguerre(n, m*n) ~ sqrt(1/2 + (m-2)/(2*sqrt(m*(m-4)))) * exp((m - 2 - sqrt(m*(m-4)))*n/2) * ((m - 2 + sqrt(m*(m-4)))/2)^n * n^n.

%H Vaclav Kotesovec, <a href="/A332695/b332695.txt">Table of n, a(n) for n = 0..310</a>

%F a(n) ~ sqrt(1/2 + 1/sqrt(3)) * 2^n * exp((2-sqrt(3))*n) * ((1 + sqrt(3))/2)^(2*n) * n^n.

%t Table[(-1)^n * n! * LaguerreL[n, 6*n], {n, 0, 20}]

%t Flatten[{1, Table[n!*Sum[Binomial[n, k] * (-1)^(n-k) * 6^k * n^k / k!, {k, 0, n}], {n, 1, 20}]}]

%t Table[(-1)^n * n! * Hypergeometric1F1[-n, 1, 6*n], {n, 0, 20}]

%o (PARI) a(n) = (-1)^n*n!*pollaguerre(n, 0, 6*n); \\ _Michel Marcus_, Feb 05 2021

%Y Cf. A277420, A277423, A332692, A332693, A332679, A332694.

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, Feb 20 2020