A344106 a(n) = n! * LaguerreL(n, -n+1).
1, 1, 7, 86, 1473, 32344, 866695, 27422352, 1000578817, 41361536384, 1910451937671, 97512721964800, 5450486787062977, 331112639931669504, 21722219855305516807, 1530517712811373819904, 115269154497700063898625, 9241045907270523509112832, 785719407951447904088069383
Offset: 0
Keywords
Programs
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Mathematica
Table[n!*LaguerreL[n, -n+1], {n, 0, 20}] -
PARI
a(n) = n!*subst(pollaguerre(n), x, 1-n); \\ Michel Marcus, May 09 2021
Formula
a(n) ~ exp((n-1)/phi - n) * phi^(2*n+1) * n^n / 5^(1/4), where phi = A001622 = (1+sqrt(5))/2 is the golden ratio.
a(n) = Sum_{k=0..n} binomial(n, k)^2*(n - k)!*(n - 1)^k. - Peter Luschny, Dec 25 2021