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A277391
a(n) = n!*LaguerreL(n, -2*n).
11
1, 3, 34, 654, 17688, 616120, 26252496, 1322624016, 76909665664, 5069558461824, 373529452588800, 30422117430022912, 2713911389090970624, 263171888496899625984, 27563036166079327578112, 3100736138961250867968000, 372888702864658105915244544
OFFSET
0,2
LINKS
Eric Weisstein's World of Mathematics, Laguerre Polynomial
FORMULA
a(n) = n! * Sum_{k=0..n} binomial(n, k) * 2^k * n^k / k!.
a(n) ~ (1 + sqrt(3))^(2*n+1) * n^n / (3^(1/4) * 2^(n+1) * exp((2 - sqrt(3))*n)).
MATHEMATICA
Table[n!*LaguerreL[n, -2*n], {n, 0, 20}]
Flatten[{1, Table[n!*Sum[Binomial[n, k]*2^k*n^k/k!, {k, 0, n}], {n, 1, 20}]}]
PROG
(PARI) for(n=0, 30, print1(n!*sum(k=0, n, binomial(n, k)*2^k*n^k/k!), ", ")) \\ G. C. Greubel, May 15 2018
(Magma) [Factorial(n)*(&+[Binomial(n, k)*2^k*n^k/Factorial(k): k in [0..n]]): n in [0..30]]; // G. C. Greubel, May 15 2018
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Oct 12 2016
STATUS
approved