

A295182


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


3



1, 0, 2, 6, 72, 620, 8640, 122346, 2156672, 41367672, 905126400, 21646532270, 570077595648, 16268377195044, 502096929431552, 16629319748711250, 588938142209310720, 22196966267762213744, 887352465220427317248, 37496112562144553167062, 1670071417348195942400000, 78195398849926292810318940
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OFFSET

0,3


COMMENTS

The nth term of the nfold exponential convolution of A000166 with themselves.


LINKS

Robert Israel, Table of n, a(n) for n = 0..396
N. J. A. Sloane, Transforms
Index entries for sequences related to factorial numbers


FORMULA

a(n) = A295181(n,n).
a(n) ~ phi^(3*n  1/2) * n^n / (5^(1/4) * exp(n*(1 + 1/phi))), where phi = A001622 = (1+sqrt(5))/2 is the golden ratio.  Vaclav Kotesovec, Nov 16 2017


MAPLE

S:= series((exp(x)/(1x))^n, x, 30):
seq(n!*coeff(S, x, n), n=0..29); # Robert Israel, Nov 16 2017


MATHEMATICA

Table[n! SeriesCoefficient[Exp[n x]/(1  x)^n, {x, 0, n}], {n, 0, 21}]


CROSSREFS

Main diagonal of A295181.
Cf. A000166, A000407, A001813, A087981, A137775, A295183.
Sequence in context: A329965 A171582 A152885 * A052613 A156493 A218891
Adjacent sequences: A295179 A295180 A295181 * A295183 A295184 A295185


KEYWORD

nonn


AUTHOR

Ilya Gutkovskiy, Nov 16 2017


STATUS

approved



