A295183 - OEIS

%I #11 May 25 2018 04:50:28

%S 1,2,18,276,5960,165870,5648832,227507336,10577029248,557457222330,

%T 32843470246400,2139014862736092,152592485390272512,

%U 11833139429253625574,991101777088623943680,89164680959505831930000,8575295241502192869343232,877955050581430468997781234,95337079570413427211596726272

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

%C The n-th term of the n-fold exponential convolution of A000522 with themselves.

%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</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>

%H <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>

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

%F a(n) ~ phi^(3*n + 1/2) * n^n / (5^(1/4) * exp(n/phi)), where phi = A001622 = (1+sqrt(5))/2 is the golden ratio. - _Vaclav Kotesovec_, Nov 16 2017

%F a(n) = (-1)^n*n!*Laguerre(n,-2*n,n). - _Ilya Gutkovskiy_, May 24 2018

%t Table[n! SeriesCoefficient[Exp[n x]/(1 - x)^n, {x, 0, n}], {n, 0, 18}]

%Y Cf. A000407, A000522, A001813, A081923, A295182, A295188.

%K nonn

%O 0,2

%A _Ilya Gutkovskiy_, Nov 16 2017