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A277421 a(n) = n!*LaguerreL(n, -7*n). 10

%I

%S 1,8,254,13614,1025048,99368620,11781698256,1651548277946,

%T 267197019684224,49000715036948304,10044513851042988800,

%U 2275926588768085912582,564838094735322988575744,152378369304839730672573044,44397985962782115253758973952

%N a(n) = n!*LaguerreL(n, -7*n).

%H G. C. Greubel, <a href="/A277421/b277421.txt">Table of n, a(n) for n = 0..250</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LaguerrePolynomial.html">Laguerre Polynomial</a>

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

%F a(n) = n! * Sum_{k=0..n} binomial(n, k) * 7^k * n^k / k!.

%F a(n) ~ sqrt(1/2 + 9/(2*sqrt(77))) * ((9 + sqrt(77))/2)^n * exp((-9 + sqrt(77))*n/2) * n^n.

%t Table[n!*LaguerreL[n, -7*n], {n, 0, 20}]

%t Flatten[{1, Table[n!*Sum[Binomial[n, k] * 7^k * n^k / k!, {k, 0, n}], {n, 1, 20}]}]

%o (PARI) for(n=0, 30, print1(n!*sum(k=0, n, binomial(n,k)*7^k*n^k/k!), ", ")) \\ _G. C. Greubel_, May 15 2018

%o (MAGMA) [Factorial(n)*(&+[Binomial(n,k)*7^k*n^k/Factorial(k): k in [0..n]]): n in [0..30]]; // _G. C. Greubel_, May 15 2018

%Y Cf. A277373, A277391, A277392, A277418, A277419, A277420, A277422.

%Y Cf. A002720, A087912, A277382.

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, Oct 14 2016

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Last modified June 13 09:54 EDT 2021. Contains 344981 sequences. (Running on oeis4.)