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URL: https://oeis.org/A295183

⇱ A295183 - OEIS

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A295183
a(n) = n! * [x^n] exp(n*x)/(1 - x)^n.
2
1, 2, 18, 276, 5960, 165870, 5648832, 227507336, 10577029248, 557457222330, 32843470246400, 2139014862736092, 152592485390272512, 11833139429253625574, 991101777088623943680, 89164680959505831930000, 8575295241502192869343232, 877955050581430468997781234, 95337079570413427211596726272
OFFSET
0,2
COMMENTS
The n-th term of the n-fold exponential convolution of A000522 with themselves.
FORMULA
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
a(n) = (-1)^n*n!*Laguerre(n,-2*n,n). - Ilya Gutkovskiy, May 24 2018
MATHEMATICA
Table[n! SeriesCoefficient[Exp[n x]/(1 - x)^n, {x, 0, n}], {n, 0, 18}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Nov 16 2017
STATUS
approved